On Saturday, 5 August 2023 at 06:45:09 UTC-4, markus...wrote:
> > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > >
> > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > >
> > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything....
> > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > >
> > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > >
> > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > >
> > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > >
> > > > > > > > <drivel>
> > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > >
> > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > >
> > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > >
> > > > sys·tem·at·ic
> > > > adjective
> > > > done or acting according to a fixed plan or system; methodical.
> > > >
> > > > Oxford dictionary.
> > > >
> > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > >
> > > > <repeated his drivel>
> > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > Fuck off. I don't have time to teach you English.
> I know English. I don't know what that means mathematically.

lördag 5 augusti 2023 kl. 14:19:30 UTC+2 skrev Eram semper recta:
> On Saturday, 5 August 2023 at 06:45:09 UTC-4, markus...wrote:
> > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > >
> > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything....
> > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > >
> > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > >
> > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > >
> > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > >
> > > > > > > > > <drivel>
> > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > >
> > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > >
> > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > >
> > > > > sys·tem·at·ic
> > > > > adjective
> > > > > done or acting according to a fixed plan or system; methodical.
> > > > >
> > > > > Oxford dictionary.
> > > > >
> > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > >
> > > > > <repeated his drivel>
> > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > Fuck off. I don't have time to teach you English.
> > I know English. I don't know what that means mathematically.
> I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
>
> A set is countable if and only if, its elements can be systematically given UNIQUE names.
>
> Assuming you are being sincere (I also doubt this because I know you are a troll!):
>
> The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
>
> We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
>
> Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
You don't need "a next element" in order to be countable. Countable or not, the set can be equipped with any order. Being countable is not dependent on the order of the set. Q is countable, but there is no rational number after 0. Being countable means you can count the elements up in a potentially infinite list. That is, you can say what the first element is. Then what the second is, and so on. You can do this with the rational numbers. Count them up.

On Saturday, 5 August 2023 at 12:42:10 UTC-4, markus...
> lördag 5 augusti 2023 kl. 14:19:30 UTC+2 skrev Eram semper recta:
> > On Saturday, 5 August 2023 at 06:45:09 UTC-4, markus...wrote:
> > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > > >
> > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > >
> > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > >
> > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > >
> > > > > > > > > > <drivel>
> > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > >
> > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > >
> > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > >
> > > > > > sys·tem·at·ic
> > > > > > adjective
> > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > >
> > > > > > Oxford dictionary.
> > > > > >
> > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > >
> > > > > > <repeated his drivel>
> > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > Fuck off. I don't have time to teach you English.
> > > I know English. I don't know what that means mathematically.
> > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> >
> > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> >
> > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> >
> > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> >
> > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> >
> > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
> You don't need "a next element" in order to be countable.

lördag 5 augusti 2023 kl. 21:03:55 UTC+2 skrev Eram semper recta:
> On Saturday, 5 August 2023 at 12:42:10 UTC-4, markus...
> > lördag 5 augusti 2023 kl. 14:19:30 UTC+2 skrev Eram semper recta:
> > > On Saturday, 5 August 2023 at 06:45:09 UTC-4, markus...wrote:
> > > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > > >
> > > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > > >
> > > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > > >
> > > > > > > > > > > <drivel>
> > > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > > >
> > > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > > >
> > > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > > >
> > > > > > > sys·tem·at·ic
> > > > > > > adjective
> > > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > > >
> > > > > > > Oxford dictionary.
> > > > > > >
> > > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > > >
> > > > > > > <repeated his drivel>
> > > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > > Fuck off. I don't have time to teach you English.
> > > > I know English. I don't know what that means mathematically.
> > > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> > >
> > > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> > >
> > > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> > >
> > > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> > >
> > > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> > >
> > > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
> > You don't need "a next element" in order to be countable.
> Yes, you do, moron. That is what is meant by systematically naming all the elements.
>
> <shit ignored>
But your supposed bijection doesn't map 1/3 to any natural number. So how can it be any bijection?

On Saturday, 5 August 2023 at 17:27:07 UTC-4, markus..
> > > > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > > > >
> > > > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > > > >
> > > > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > > > >
> > > > > > > > > > > > <drivel>
> > > > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > > > >
> > > > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > > > >
> > > > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > > > Repeat this shit again and this discussion is also over.. I don't have time for morons.
> > > > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > > > >
> > > > > > > > sys·tem·at·ic
> > > > > > > > adjective
> > > > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > > > >
> > > > > > > > Oxford dictionary.
> > > > > > > >
> > > > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > > > >
> > > > > > > > <repeated his drivel>
> > > > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > > > Fuck off. I don't have time to teach you English.
> > > > > I know English. I don't know what that means mathematically.
> > > > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> > > >
> > > > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> > > >
> > > > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> > > >
> > > > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> > > >
> > > > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> > > >
> > > > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
> > > You don't need "a next element" in order to be countable.
> > Yes, you do, moron. That is what is meant by systematically naming all the elements.
> >
> > <shit ignored>
> But your supposed bijection doesn't map 1/3 to any natural number. So how can it be any bijection?

söndag 6 augusti 2023 kl. 02:07:34 UTC+2 skrev Eram semper recta:
> On Saturday, 5 August 2023 at 17:27:07 UTC-4, markus..
> > > > > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > > > > > I have both, you little moron.. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits.. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits..
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO.. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another.. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable..
> > > > > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > > > > >
> > > > > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > > > > >
> > > > > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > > > > >
> > > > > > > > > > > > > <drivel>
> > > > > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > > > > >
> > > > > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > > > > >
> > > > > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > > > > >
> > > > > > > > > sys·tem·at·ic
> > > > > > > > > adjective
> > > > > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > > > > >
> > > > > > > > > Oxford dictionary.
> > > > > > > > >
> > > > > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > > > > >
> > > > > > > > > <repeated his drivel>
> > > > > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > > > > Fuck off. I don't have time to teach you English.
> > > > > > I know English. I don't know what that means mathematically.
> > > > > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> > > > >
> > > > > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> > > > >
> > > > > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> > > > >
> > > > > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> > > > >
> > > > > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> > > > >
> > > > > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
> > > > You don't need "a next element" in order to be countable.
> > > Yes, you do, moron. That is what is meant by systematically naming all the elements.
> > >
> > > <shit ignored>
> > But your supposed bijection doesn't map 1/3 to any natural number. So how can it be any bijection?
> Doesn't have to. For any 0.3 with n threes you give me, I give you a unique name. 1/3 has no measure in base 10. If you claim that 0.333... is not in my tree, then you are saying that 1/3 has no infinite decimal expansion and thus contradicting your earlier claims.
0.333... is indeed in your tree but doesn't correspond to an integer.

On Sunday, 6 August 2023 at 14:20:35 UTC-4, markus...@gmail.com wrote:
> söndag 6 augusti 2023 kl. 02:07:34 UTC+2 skrev Eram semper recta:
> > On Saturday, 5 August 2023 at 17:27:07 UTC-4, markus..
> > > > > > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements..
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > <drivel>
> > > > > > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > > > > > >
> > > > > > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > > > > > >
> > > > > > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > > > > > >
> > > > > > > > > > sys·tem·at·ic
> > > > > > > > > > adjective
> > > > > > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > > > > > >
> > > > > > > > > > Oxford dictionary.
> > > > > > > > > >
> > > > > > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > > > > > >
> > > > > > > > > > <repeated his drivel>
> > > > > > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > > > > > Fuck off. I don't have time to teach you English.
> > > > > > > I know English. I don't know what that means mathematically.
> > > > > > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> > > > > >
> > > > > > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> > > > > >
> > > > > > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> > > > > >
> > > > > > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> > > > > >
> > > > > > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> > > > > >
> > > > > > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
> > > > > You don't need "a next element" in order to be countable.
> > > > Yes, you do, moron. That is what is meant by systematically naming all the elements.
> > > >
> > > > <shit ignored>
> > > But your supposed bijection doesn't map 1/3 to any natural number. So how can it be any bijection?
> > Doesn't have to. For any 0.3 with n threes you give me, I give you a unique name. 1/3 has no measure in base 10. If you claim that 0.333... is not in my tree, then you are saying that 1/3 has no infinite decimal expansion and thus contradicting your earlier claims.
> 0.333... is indeed in your tree but doesn't correspond to an integer.

måndag 7 augusti 2023 kl. 00:33:01 UTC+2 skrev Eram semper recta:
> On Sunday, 6 August 2023 at 14:20:35 UTC-4, markus...@gmail.com wrote:
> > söndag 6 augusti 2023 kl. 02:07:34 UTC+2 skrev Eram semper recta:
> > > On Saturday, 5 August 2023 at 17:27:07 UTC-4, markus..
> > > > > > > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > > > > > > Rubbish. Try naming the elements of R.. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > <drivel>
> > > > > > > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > > > > > > >
> > > > > > > > > > > sys·tem·at·ic
> > > > > > > > > > > adjective
> > > > > > > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > > > > > > >
> > > > > > > > > > > Oxford dictionary.
> > > > > > > > > > >
> > > > > > > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > > > > > > >
> > > > > > > > > > > <repeated his drivel>
> > > > > > > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > > > > > > Fuck off. I don't have time to teach you English.
> > > > > > > > I know English. I don't know what that means mathematically..
> > > > > > > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> > > > > > >
> > > > > > > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> > > > > > >
> > > > > > > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> > > > > > >
> > > > > > > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> > > > > > >
> > > > > > > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> > > > > > >
> > > > > > > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
> > > > > > You don't need "a next element" in order to be countable.
> > > > > Yes, you do, moron. That is what is meant by systematically naming all the elements.
> > > > >
> > > > > <shit ignored>
> > > > But your supposed bijection doesn't map 1/3 to any natural number. So how can it be any bijection?
> > > Doesn't have to. For any 0.3 with n threes you give me, I give you a unique name. 1/3 has no measure in base 10. If you claim that 0.333... is not in my tree, then you are saying that 1/3 has no infinite decimal expansion and thus contradicting your earlier claims.
> > 0.333... is indeed in your tree but doesn't correspond to an integer.
> You've had a change of mind? Chuckle.
>
> It very much corresponds to an integer. For all the digits you give me, I give you a unique name or identifier and I add "..." just as you do when you write shit like 0.333 and you append "...". No difference whatsoever.
> > It doesn't appear on your list of real numbers.
> Well, none of those are real numbers because there is no such thing as an infinite decimal expansion, only in your syphilis infected brain.
I agree that 1/3 could correspond to an infinite string of digits. But no natural number has an infinite amount of digits.

On Monday, 7 August 2023 at 05:01:24 UTC-4, markus...@gmail.com wrote:
> måndag 7 augusti 2023 kl. 00:33:01 UTC+2 skrev Eram semper recta:
> > On Sunday, 6 August 2023 at 14:20:35 UTC-4, markus...@gmail.com wrote:
> > > söndag 6 augusti 2023 kl. 02:07:34 UTC+2 skrev Eram semper recta:
> > > > On Saturday, 5 August 2023 at 17:27:07 UTC-4, markus..
> > > > > > > > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection.
> > > > > > > > > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare..
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > <drivel>
> > > > > > > > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > > > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > > > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > > > > > > > >
> > > > > > > > > > > > sys·tem·at·ic
> > > > > > > > > > > > adjective
> > > > > > > > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > > > > > > > >
> > > > > > > > > > > > Oxford dictionary.
> > > > > > > > > > > >
> > > > > > > > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > > > > > > > >
> > > > > > > > > > > > <repeated his drivel>
> > > > > > > > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > > > > > > > Fuck off. I don't have time to teach you English.
> > > > > > > > > I know English. I don't know what that means mathematically.
> > > > > > > > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> > > > > > > >
> > > > > > > > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> > > > > > > >
> > > > > > > > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> > > > > > > >
> > > > > > > > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> > > > > > > >
> > > > > > > > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> > > > > > > >
> > > > > > > > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't..
> > > > > > > You don't need "a next element" in order to be countable.
> > > > > > Yes, you do, moron. That is what is meant by systematically naming all the elements.
> > > > > >
> > > > > > <shit ignored>
> > > > > But your supposed bijection doesn't map 1/3 to any natural number.. So how can it be any bijection?
> > > > Doesn't have to. For any 0.3 with n threes you give me, I give you a unique name. 1/3 has no measure in base 10. If you claim that 0.333... is not in my tree, then you are saying that 1/3 has no infinite decimal expansion and thus contradicting your earlier claims.
> > > 0.333... is indeed in your tree but doesn't correspond to an integer.
> > You've had a change of mind? Chuckle.
> >
> > It very much corresponds to an integer. For all the digits you give me, I give you a unique name or identifier and I add "..." just as you do when you write shit like 0.333 and you append "...". No difference whatsoever.
> > > It doesn't appear on your list of real numbers.
> > Well, none of those are real numbers because there is no such thing as an infinite decimal expansion, only in your syphilis infected brain.
> I agree that 1/3 could correspond to an infinite string of digits. But no natural number has an infinite amount of digits.

måndag 7 augusti 2023 kl. 14:31:00 UTC+2 skrev Eram semper recta:
> On Monday, 7 August 2023 at 05:01:24 UTC-4, markus...@gmail.com wrote:
> > måndag 7 augusti 2023 kl. 00:33:01 UTC+2 skrev Eram semper recta:
> > > On Sunday, 6 August 2023 at 14:20:35 UTC-4, markus...@gmail.com wrote:
> > > > söndag 6 augusti 2023 kl. 02:07:34 UTC+2 skrev Eram semper recta:
> > > > > On Saturday, 5 August 2023 at 17:27:07 UTC-4, markus..
> > > > > > > > > > > > > > > > > > > > > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > > > > > > > > > > > > > > > > > > > > > You have a representation of the numbers in (0, 1), but not an enumeration. So not a bijection..
> > > > > > > > > > > > > > > > > > > > > > > > > > > I have both, you little moron. Representation is enumeration.
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > Has nothing to do with a "bijection".
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > To be countable means to be listable in a systematic way.
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > Eat shit and die.
> > > > > > > > > > > > > > > > > > > > > > > > > > Then tell me what natural number one third corresponds to.
> > > > > > > > > > > > > > > > > > > > > > > > > If you actually studied real analysis, then you would know the answer to your question.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Like I said, you are a very sick boy and you need to seek help immediately. Sweden has free healthcare.
> > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > Get help soon.
> > > > > > > > > > > > > > > > > > > > > > > > Why would I need help?
> > > > > > > > > > > > > > > > > > > > > > > Mentally ill people don't know why they need help, so no use asking. Just get help because you are one heck of an annoying, delusional crank!
> > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > Can't you just tell me where 1/3 is in your list? What natural number does it correspond to?
> > > > > > > > > > > > > > > > > > > > > > > It does not have to correspond to a natural number. That is not the principle of sets which are countable.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > A countable set is one whose elements can be SYSTEMATICALLY listed or NAMED UNIQUELY. The set of natural numbers has his property and that is why it is used as an INDEX set. Your baboon lecturers didn't know these things and that is why you are such a moron.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > The elements in my tree are named by the top-down and left-right traversals.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > As for 1/3, it has no measure in base 10. If you ask me to show you, then I'll ask you to give me all the digits. As long as you keep giving me significant digits, I can keep giving you a unique NAME.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > For any decimal representation, I can give you a unique name in the tree, but you have to provide all the digits.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > You can't respond like the moron that you are, that there are infinite representations because there aren't.
> > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > Irony is that you won't even notice you are contradicting yourself when you claim 0.333... is an infinite representation and then assert it is not in my tree. I piss and shit on you! LMAO. I assert that 0.333... is in my tree.
> > > > > > > > > > > > > > > > > > > > > > It does have to correspond with a natural number. That's what s bijection is.
> > > > > > > > > > > > > > > > > > > > > Pay attention to what I tell you, you pigheaded moron. A bijection is the same as an INDEX from one set into another. It is a way of checking for countability, but countability does not care about the natural numbers, only that a set's elements can be systematically NAMED and UNIQUE.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > I agree that 1/3 is in your tree, but it doesn't have a corresponding natural number.
> > > > > > > > > > > > > > > > > > > > > Does not need to. All one needs is a unique NAME at each node in the tree.
> > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > 0.333... does not have a corresponding fraction of the form p/10^n.
> > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > Every element of any set can be "named", so that's why it's not a good definition.
> > > > > > > > > > > > > > > > > > > > > Rubbish. Try naming the elements of R. It is a very solid definition. Better than crank Cantor's by far.
> > > > > > > > > > > > > > > > > > > > > > The correct definition is that every element corresponds to a natural number and every natural number corresponds to an element.
> > > > > > > > > > > > > > > > > > > > > No. That's what your teacher tells you because like you, he does not understand what it means for a set to be countable, only how to check for countability. Just like you, moron! You have no clue what it means for a set to be countable. Wait, you have no clue about anything...
> > > > > > > > > > > > > > > > > > > > Every real number can be "named" by their decimal expansion.
> > > > > > > > > > > > > > > > > > > That is one of your illusions. Even if it were true, it still would not be enough to prove that R is countable. Like I taught you, moron, you need to be able to SYSTEMATICALLY NAME the elements.
> > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > You do not have a natural number for 1/3, so it isn't a proof that the reals are countable. It's wrong.
> > > > > > > > > > > > > > > > > > > Nope. It's correct. The one who is ALWAYS wrong is you. I kicked you off Discord not because you were always wrong, but because you never learn. Tsk, tsk. True crank is what you are.,
> > > > > > > > > > > > > > > > > > I can systematically "name" every element of R (which by the way isn't a formal definition), that doesn't make R countable.
> > > > > > > > > > > > > > > > > You can't. It's not a formal definition but then again, Cantor was not a genius. I am. You on the other hand, are a moron.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > If you think you can name every element of R, then do it here, you lying blowhard idiot!
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > YES, it and it alone makes a set countable. N has this special property that all its elements can be named uniquely in a given radix system. This is not possible with the imaginary set R.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > <drivel>
> > > > > > > > > > > > > > > > Every real number can be named by its full decimal expansion, for example.
> > > > > > > > > > > > > > > Put up or shut the fuck up, you stupid! Show how you can systematically name every real number using your "full" decimal expansions.
> > > > > > > > > > > > > > > > A decimal expansion uniquely defines a real number.
> > > > > > > > > > > > > > > No such thing as infinite decimal expansion, so no real number.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > But 'being named" isn't mathematics since you haven't given a formal definition for that.
> > > > > > > > > > > > > > > You don't get to decide what is mathematics or not, you motherless fuck!
> > > > > > > > > > > > > > > The definition I gave is 100% mathematics. The one you use (bijection with N) is for stupids like you and your professors.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > You haven't proved the reals are countable because you do not have a bijection. 🥸
> > > > > > > > > > > > > > > Repeat this shit again and this discussion is also over. I don't have time for morons.
> > > > > > > > > > > > > > Well, you haven't really defined what "systematically name" means in formal logic.
> > > > > > > > > > > > > Sonny, I don't have time to teach you English in addition to mathematics. There are good dictionaries online. Try using them!
> > > > > > > > > > > > >
> > > > > > > > > > > > > sys·tem·at·ic
> > > > > > > > > > > > > adjective
> > > > > > > > > > > > > done or acting according to a fixed plan or system; methodical.
> > > > > > > > > > > > >
> > > > > > > > > > > > > Oxford dictionary.
> > > > > > > > > > > > >
> > > > > > > > > > > > > What is quite laughable is that you claim to have a BS in math and you don't understand "systematically"! May be time for you to join Zelos Malum for some English classes? LMAO.
> > > > > > > > > > > > >
> > > > > > > > > > > > > <repeated his drivel>
> > > > > > > > > > > > What does "done or acting according to a fixed plan or system" mean FORMALLY?
> > > > > > > > > > > Fuck off. I don't have time to teach you English.
> > > > > > > > > > I know English. I don't know what that means mathematically.
> > > > > > > > > I doubt it, but if you knew ANY mathematics whatsoever, then you would know exactly what it means to say:
> > > > > > > > >
> > > > > > > > > A set is countable if and only if, its elements can be systematically given UNIQUE names.
> > > > > > > > >
> > > > > > > > > Assuming you are being sincere (I also doubt this because I know you are a troll!):
> > > > > > > > >
> > > > > > > > > The "set" of natural numbers is countable because its members can be given unique names in a systematic way.
> > > > > > > > >
> > > > > > > > > We start of with the first element which is one and we call it '1'. The next element is called '2', and so on. This way we can assign unique names from any radix system for the elements beginning with the first and as far as we like.
> > > > > > > > >
> > > > > > > > > Contrast this with your imaginary set R. Are you able to start with 0 and then name all the consecutive elements? No, crank. You can't.
> > > > > > > > You don't need "a next element" in order to be countable.
> > > > > > > Yes, you do, moron. That is what is meant by systematically naming all the elements.
> > > > > > >
> > > > > > > <shit ignored>
> > > > > > But your supposed bijection doesn't map 1/3 to any natural number. So how can it be any bijection?
> > > > > Doesn't have to. For any 0.3 with n threes you give me, I give you a unique name. 1/3 has no measure in base 10. If you claim that 0.333... is not in my tree, then you are saying that 1/3 has no infinite decimal expansion and thus contradicting your earlier claims.
> > > > 0.333... is indeed in your tree but doesn't correspond to an integer.
> > > You've had a change of mind? Chuckle.
> > >
> > > It very much corresponds to an integer. For all the digits you give me, I give you a unique name or identifier and I add "..." just as you do when you write shit like 0.333 and you append "...". No difference whatsoever..
> > > > It doesn't appear on your list of real numbers.
> > > Well, none of those are real numbers because there is no such thing as an infinite decimal expansion, only in your syphilis infected brain.
> > I agree that 1/3 could correspond to an infinite string of digits. But no natural number has an infinite amount of digits.
> As I have repeatedly said and will say this LAST time: natural numbers have NOTHING to do with the fundamental concept of set countability. The set N is used because it itself is countable and acts as an INDEX set.
>
> A set is countable if and only if, its members can be uniquely and systematically named or listed.
>
> THIS AND NOTHING ELSE. I can't help it your teachers were morons.
> >
> > It doesn't correspond to a NATURAL NUMBER. That's the issue.
> NO! It's not an issue at all. All it needs to correspond to is a unique label or name. That's it.
>
> This discussion is over.
It doesn't even converge to an infinite string.

On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument

I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.

Morons have never asked themselves why Cantor chose N as an index set.

tisdag 8 augusti 2023 kl. 03:07:29 UTC+2 skrev Eram semper recta:
> On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
>
> I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
>
> Morons have never asked themselves why Cantor chose N as an index set.
It's because you can list them in a list starting from 1, 2, 3, ...

But 1/3 will not appear on your list.

On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
>
> I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
>
> Morons have never asked themselves why Cantor chose N as an index set.

Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".

To actually investigate whether any definition is well-formed or not, has no relevance to them.

tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> >
> > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> >
> > Morons have never asked themselves why Cantor chose N as an index set.
> Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
>
> To actually investigate whether any definition is well-formed or not, has no relevance to them.
I just gave you the intuition behind the definition.

On Tuesday, August 8, 2023 at 6:36:23 PM UTC+2, Eram semper recta wrote:

> To actually investigate whether any definition is well-formed or not, has no relevance to them.

Holy shit! You are fantasizing.

<facepalm>

See: https://en.wikipedia.org/wiki/Delusion

On Tuesday, August 8, 2023 at 3:07:29 AM UTC+2, Eram semper recta wrote:

> what it means for a set to be countable.

What it means is specified by the DEFINITION of the term "countable", imbecile.

"In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers." (Wikipedia)

On the other hand, this rather precise definition can be relaxed somehow in the context of "math lingo":

"A set is said to be countable, if you can make a list of its members. By a list we mean that you can find a first member, a second one, and so on, and eventually assign to each member an integer of its own, perhaps going on forever."

Source: https://math.mit.edu/~djk/calculus_beginners/chapter01/section04.html

Sounds very much like your definition:

"A set is countable if and only if, its members can be [...] listed."

> Morons have never asked themselves why Cantor chose N as an index set.

Seems that you _intimately_ know all morons. Fascinating!

On Tuesday, 8 August 2023 at 20:17:48 UTC-4, Fritz Feldhase wrote:
> On Tuesday, August 8, 2023 at 6:36:23 PM UTC+2, Eram semper recta wrote:
>
> > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> Holy shit! You are fantasizing.

No stupid. That is your projection. I am not like you.

>
> <facepalm>
>
> See: https://en.wikipedia.org/wiki/Delusion

tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> >
> > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> >
> > Morons have never asked themselves why Cantor chose N as an index set.
> Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
>
> To actually investigate whether any definition is well-formed or not, has no relevance to them.
To see if something is well-defined or not is the very essence of mathematics.

On Wednesday, 9 August 2023 at 05:23:32 UTC-4, markus...@gmail.com wrote:
> tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> > On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > >
> > > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> > >
> > > Morons have never asked themselves why Cantor chose N as an index set..
> > Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
> >
> > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> To see if something is well-defined or not is the very essence of mathematics.

There is so much irony in that coming from a troll like you! Boy, you have no clue what it means for a concept to be well-formed.

onsdag 9 augusti 2023 kl. 13:15:43 UTC+2 skrev Eram semper recta:
> On Wednesday, 9 August 2023 at 05:23:32 UTC-4, markus...@gmail.com wrote:
> > tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> > > On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > > > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > >
> > > > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> > > >
> > > > Morons have never asked themselves why Cantor chose N as an index set.
> > > Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
> > >
> > > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> > To see if something is well-defined or not is the very essence of mathematics.
> There is so much irony in that coming from a troll like you! Boy, you have no clue what it means for a concept to be well-formed.
Any system that isn't self-contradictory is well-defined.

On Wednesday, 9 August 2023 at 15:48:39 UTC-4, markus...@gmail.com wrote:
> onsdag 9 augusti 2023 kl. 13:15:43 UTC+2 skrev Eram semper recta:
> > On Wednesday, 9 August 2023 at 05:23:32 UTC-4, markus...@gmail.com wrote:
> > > tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> > > > On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > > > > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > >
> > > > > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> > > > >
> > > > > Morons have never asked themselves why Cantor chose N as an index set.
> > > > Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
> > > >
> > > > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> > > To see if something is well-defined or not is the very essence of mathematics.
> > There is so much irony in that coming from a troll like you! Boy, you have no clue what it means for a concept to be well-formed.
> Any system that isn't self-contradictory is well-defined.

No. That is nonsense. Thankfully the Ancient Greeks rejected such garbage otherwise there would be no mathematics at all today.

onsdag 9 augusti 2023 kl. 22:25:42 UTC+2 skrev Eram semper recta:
> On Wednesday, 9 August 2023 at 15:48:39 UTC-4, markus...@gmail.com wrote:
> > onsdag 9 augusti 2023 kl. 13:15:43 UTC+2 skrev Eram semper recta:
> > > On Wednesday, 9 August 2023 at 05:23:32 UTC-4, markus...@gmail.com wrote:
> > > > tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> > > > > On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > > > > > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > >
> > > > > > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> > > > > >
> > > > > > Morons have never asked themselves why Cantor chose N as an index set.
> > > > > Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
> > > > >
> > > > > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> > > > To see if something is well-defined or not is the very essence of mathematics.
> > > There is so much irony in that coming from a troll like you! Boy, you have no clue what it means for a concept to be well-formed.
> > Any system that isn't self-contradictory is well-defined.
> No. That is nonsense. Thankfully the Ancient Greeks rejected such garbage otherwise there would be no mathematics at all today.
Classical mathematics is quite primitive. Math has evolved 2000 years since..

On Wednesday, 9 August 2023 at 17:31:42 UTC-4, markus...@gmail.com wrote:
> onsdag 9 augusti 2023 kl. 22:25:42 UTC+2 skrev Eram semper recta:
> > On Wednesday, 9 August 2023 at 15:48:39 UTC-4, markus...@gmail.com wrote:
> > > onsdag 9 augusti 2023 kl. 13:15:43 UTC+2 skrev Eram semper recta:
> > > > On Wednesday, 9 August 2023 at 05:23:32 UTC-4, markus...@gmail.com wrote:
> > > > > tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> > > > > > On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > > > > > > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > >
> > > > > > > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> > > > > > >
> > > > > > > Morons have never asked themselves why Cantor chose N as an index set.
> > > > > > Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
> > > > > >
> > > > > > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> > > > > To see if something is well-defined or not is the very essence of mathematics.
> > > > There is so much irony in that coming from a troll like you! Boy, you have no clue what it means for a concept to be well-formed.
> > > Any system that isn't self-contradictory is well-defined.
> > No. That is nonsense. Thankfully the Ancient Greeks rejected such garbage otherwise there would be no mathematics at all today.
> Classical mathematics is quite primitive. Math has evolved 2000 years since.

Idiot thinks I am going to have a discussion with him. Gosh, what a moron! LMAO.

On Thursday, August 10, 2023 at 1:06:47 AM UTC+2, Eram semper recta wrote:
> On Wednesday, 9 August 2023 at 17:31:42 UTC-4, markus...@gmail.com wrote:
> > onsdag 9 augusti 2023 kl. 22:25:42 UTC+2 skrev Eram semper recta:
> > > On Wednesday, 9 August 2023 at 15:48:39 UTC-4, markus...@gmail.com wrote:
> > > > onsdag 9 augusti 2023 kl. 13:15:43 UTC+2 skrev Eram semper recta:
> > > > > On Wednesday, 9 August 2023 at 05:23:32 UTC-4, markus...@gmail.com wrote:
> > > > > > tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> > > > > > > On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > > > > > > > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > >
> > > > > > > > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> > > > > > > >
> > > > > > > > Morons have never asked themselves why Cantor chose N as an index set.
> > > > > > > Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
> > > > > > >
> > > > > > > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> > > > > > To see if something is well-defined or not is the very essence of mathematics.
> > > > > There is so much irony in that coming from a troll like you! Boy, you have no clue what it means for a concept to be well-formed.
> > > > Any system that isn't self-contradictory is well-defined.
> > > No. That is nonsense. Thankfully the Ancient Greeks rejected such garbage otherwise there would be no mathematics at all today.
> > Classical mathematics is quite primitive. Math has evolved 2000 years since.
> Idiot thinks I am going to have a discussion with him. Gosh, what a moron! LMAO.

There's literally no discussion to be had here when 2 sides have different definitions of countability. Nevertheless one can try to motivate Cantor's definition of countability by insightful results that follow. For example, from this definition we deduce that there exists unrecognised langauges, such as the halting problem. So cut the trash talk and move on to something actually contestable.

On Wednesday, 9 August 2023 at 20:31:34 UTC-4, Kevin S wrote:
> On Thursday, August 10, 2023 at 1:06:47 AM UTC+2, Eram semper recta wrote:
> > On Wednesday, 9 August 2023 at 17:31:42 UTC-4, markus...@gmail.com wrote:
> > > onsdag 9 augusti 2023 kl. 22:25:42 UTC+2 skrev Eram semper recta:
> > > > On Wednesday, 9 August 2023 at 15:48:39 UTC-4, markus...@gmail.com wrote:
> > > > > onsdag 9 augusti 2023 kl. 13:15:43 UTC+2 skrev Eram semper recta:
> > > > > > On Wednesday, 9 August 2023 at 05:23:32 UTC-4, markus...@gmail.com wrote:
> > > > > > > tisdag 8 augusti 2023 kl. 18:36:23 UTC+2 skrev Eram semper recta:
> > > > > > > > On Monday, 7 August 2023 at 21:07:29 UTC-4, Eram semper recta wrote:
> > > > > > > > > On Tuesday, 1 August 2023 at 08:02:45 UTC-4, Eram semper recta wrote:
> > > > > > > > > > https://www.academia.edu/105144840/Cantors_Misguided_Diagonal_Argument
> > > > > > > > >
> > > > > > > > > I have never met a single mainstream math academic who has ever understood what it means for a set to be countable.
> > > > > > > > >
> > > > > > > > > Morons have never asked themselves why Cantor chose N as an index set.
> > > > > > > > Macademics are sheep. They simply accept definitions whether they are ill-formed (bad) or well-formed (good). It has never crossed their sewer brains why Cantor chose N as an index set. For this they have no answer, only an ineffective and weak response "That's the definition".
> > > > > > > >
> > > > > > > > To actually investigate whether any definition is well-formed or not, has no relevance to them.
> > > > > > > To see if something is well-defined or not is the very essence of mathematics.
> > > > > > There is so much irony in that coming from a troll like you! Boy, you have no clue what it means for a concept to be well-formed.
> > > > > Any system that isn't self-contradictory is well-defined.
> > > > No. That is nonsense. Thankfully the Ancient Greeks rejected such garbage otherwise there would be no mathematics at all today.
> > > Classical mathematics is quite primitive. Math has evolved 2000 years since.
> > Idiot thinks I am going to have a discussion with him. Gosh, what a moron! LMAO.
> There's literally no discussion to be had here when 2 sides have different definitions of countability.

There is no difference in the definitions. In the following short chat I prove that my definition of countability is the more meaningful and reliable one.

https://chat.openai.com/c/b2f6948c-f5b1-4960-8c45-1ce4f82616cb

> Nevertheless one can try to motivate Cantor's definition of countability by insightful results that follow. For example, from this definition we deduce that there exists unrecognised langauges, such as the halting problem. So cut the trash talk and move on to something actually contestable.