On Wednesday, 30 August 2023 at 19:23:58 UTC-4, markus> > > > > > > > > > > > > > > > > > > > > > > > > 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.
> > > > > > > > > > > > > > > I have to agree, but this is a persistent problem with John. He does not use the usual definitions in math, and usually invents his own (non-working definitions). Let me give me a couple of examples:
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > 1. when discussing countability, he invents his own (quite vague definition) and then claims victory whenever the other person does not use the same definition.
> > > > > > > > > > > > > > You little bastard! Enjoy lying again?
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > I said: A set is countable if and only if, its members can be systematically assigned unique names.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > That is exactly the correct definition. The one you are taught about one-to-one with N is due to the fact that you are too stupid to understand the correct definition. One-to-one with N works because N is countable and N is countable because its elements can be systematically assigned unique names.
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > <Your drivel is ignored>
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > Try to stop being the little cunt that you are and lying about what I said and did not say, you vile little bastard!
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > DIE QUICKLY!!!
> > > > > > > > > > > > > What does it mean to "systematically assigned unique names"? Injection into N?
> > > > > > > > > > > > Dumb fuckwad!
> > > > > > > > > > > >
> > > > > > > > > > > > https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
> > > > > > > > > > > https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
> > > > > > > > > > What does it mean to "index" a set, in your own words?
> > > > > > > > > Study the article, you retard! The answer is there 'in my words', moron!
> > > > > > > > The fucking imbecile Klyver doesn't realise that a one-to-one correspondence with N is the same as indexing. It takes genius to realise that indexing is just another way of systematically naming elements of another set.
> > > > > > > >
> > > > > > > > You can't fix stupid!
> > > > > > > If you use the same definition, then R isn't countable.
> > > > > > That's what I have been telling you, idiot! PAY ATTENTION.
> > > > > >
> > > > > > R is not countable because its elements cannot be systematically named.
> > > > > >
> > > > > > N is countable because its elements can be systematically named.. That is why Cantor chose N as index set.
> > > > > >
> > > > > > Think moron, think.
> > > > > If you use the mainstream definition, then R is not countable contrary to your claim.
> > > > If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. However, contrary to your lies about me having made a claim that R is countable, I have shown that R is not countable by using the correct definition:
> > > >
> > > > A set is countable if and only if, it's members can be systematically named (each name must be unique).
> > > >
> > > > And this is why N is countable, because it conforms to the above definition.
> > > >
> > > > DIE QUICKLY! You moronic piece of shit!!!
> > >
> > > "If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. "
> > > No, you haven't. You have shown that real numbers with a finite representation are countable. One third is not on your list, John. Try again. Think better next time.
> > It's too bad that you are butt-hurt because you thought you understood, but the fact is that you shouldn't be trying to do any mathematics. You're simply inept.
> Which index does 1/3 correspond to?

On what tree branch is 0.333...., you fucking moron?!!!!!

You agreed with Mark Chu Carroll that 0.333... is in my tree. On what level is it, you little pisshead????!?!!!!

torsdag 31 augusti 2023 kl. 11:56:37 UTC+2 skrev Eram semper recta:
> On Wednesday, 30 August 2023 at 19:23:58 UTC-4, markus> > > > > > > > > > > > > > > > > > > > > > > > > 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.
> > > > > > > > > > > > > > > > I have to agree, but this is a persistent problem with John. He does not use the usual definitions in math, and usually invents his own (non-working definitions). Let me give me a couple of examples:
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > 1. when discussing countability, he invents his own (quite vague definition) and then claims victory whenever the other person does not use the same definition.
> > > > > > > > > > > > > > > You little bastard! Enjoy lying again?
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > I said: A set is countable if and only if, its members can be systematically assigned unique names.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > That is exactly the correct definition. The one you are taught about one-to-one with N is due to the fact that you are too stupid to understand the correct definition. One-to-one with N works because N is countable and N is countable because its elements can be systematically assigned unique names.
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > <Your drivel is ignored>
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > Try to stop being the little cunt that you are and lying about what I said and did not say, you vile little bastard!
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > DIE QUICKLY!!!
> > > > > > > > > > > > > > What does it mean to "systematically assigned unique names"? Injection into N?
> > > > > > > > > > > > > Dumb fuckwad!
> > > > > > > > > > > > >
> > > > > > > > > > > > > https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
> > > > > > > > > > > > https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
> > > > > > > > > > > What does it mean to "index" a set, in your own words?
> > > > > > > > > > Study the article, you retard! The answer is there 'in my words', moron!
> > > > > > > > > The fucking imbecile Klyver doesn't realise that a one-to-one correspondence with N is the same as indexing. It takes genius to realise that indexing is just another way of systematically naming elements of another set.
> > > > > > > > >
> > > > > > > > > You can't fix stupid!
> > > > > > > > If you use the same definition, then R isn't countable.
> > > > > > > That's what I have been telling you, idiot! PAY ATTENTION.
> > > > > > >
> > > > > > > R is not countable because its elements cannot be systematically named.
> > > > > > >
> > > > > > > N is countable because its elements can be systematically named. That is why Cantor chose N as index set.
> > > > > > >
> > > > > > > Think moron, think.
> > > > > > If you use the mainstream definition, then R is not countable contrary to your claim.
> > > > > If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. However, contrary to your lies about me having made a claim that R is countable, I have shown that R is not countable by using the correct definition:
> > > > >
> > > > > A set is countable if and only if, it's members can be systematically named (each name must be unique).
> > > > >
> > > > > And this is why N is countable, because it conforms to the above definition.
> > > > >
> > > > > DIE QUICKLY! You moronic piece of shit!!!
> > > >
> > > > "If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. "
> > > > No, you haven't. You have shown that real numbers with a finite representation are countable. One third is not on your list, John. Try again. Think better next time.
> > > It's too bad that you are butt-hurt because you thought you understood, but the fact is that you shouldn't be trying to do any mathematics. You're simply inept.
> > Which index does 1/3 correspond to?
> On what tree branch is 0.333...., you fucking moron?!!!!!
>
> You agreed with Mark Chu Carroll that 0.333... is in my tree. On what level is it, you little pisshead????!?!!!!

Sure, it is in the tree but it doesn't correspond to a natural number.

I don't know who Chu Carroll is, but a Google search revealed he's a math professor. Have you had a discussion with him and he also brought up this point? Yes, in that case I think we agree.

But I don't know who it is and I haven't seen your discussion.

I agree that 1/3 is in the tree (not as a node or course, but as an entire path). I do not agree you have a bijection. 1/3 doesn't correspond to any natural number.

On Thursday, 31 August 2023 at 06:24:02 UTC-4, mark
> > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > 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.
> > > > > > > > > > > > > > > > > I have to agree, but this is a persistent problem with John. He does not use the usual definitions in math, and usually invents his own (non-working definitions). Let me give me a couple of examples:
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > 1. when discussing countability, he invents his own (quite vague definition) and then claims victory whenever the other person does not use the same definition.
> > > > > > > > > > > > > > > > You little bastard! Enjoy lying again?
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > I said: A set is countable if and only if, its members can be systematically assigned unique names.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > That is exactly the correct definition. The one you are taught about one-to-one with N is due to the fact that you are too stupid to understand the correct definition. One-to-one with N works because N is countable and N is countable because its elements can be systematically assigned unique names.
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > <Your drivel is ignored>
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > Try to stop being the little cunt that you are and lying about what I said and did not say, you vile little bastard!
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > DIE QUICKLY!!!
> > > > > > > > > > > > > > > What does it mean to "systematically assigned unique names"? Injection into N?
> > > > > > > > > > > > > > Dumb fuckwad!
> > > > > > > > > > > > > >
> > > > > > > > > > > > > > https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
> > > > > > > > > > > > > https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
> > > > > > > > > > > > What does it mean to "index" a set, in your own words?
> > > > > > > > > > > Study the article, you retard! The answer is there 'in my words', moron!
> > > > > > > > > > The fucking imbecile Klyver doesn't realise that a one-to-one correspondence with N is the same as indexing. It takes genius to realise that indexing is just another way of systematically naming elements of another set.
> > > > > > > > > >
> > > > > > > > > > You can't fix stupid!
> > > > > > > > > If you use the same definition, then R isn't countable.
> > > > > > > > That's what I have been telling you, idiot! PAY ATTENTION.
> > > > > > > >
> > > > > > > > R is not countable because its elements cannot be systematically named.
> > > > > > > >
> > > > > > > > N is countable because its elements can be systematically named. That is why Cantor chose N as index set.
> > > > > > > >
> > > > > > > > Think moron, think.
> > > > > > > If you use the mainstream definition, then R is not countable contrary to your claim.
> > > > > > If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. However, contrary to your lies about me having made a claim that R is countable, I have shown that R is not countable by using the correct definition:
> > > > > >
> > > > > > A set is countable if and only if, it's members can be systematically named (each name must be unique).
> > > > > >
> > > > > > And this is why N is countable, because it conforms to the above definition.
> > > > > >
> > > > > > DIE QUICKLY! You moronic piece of shit!!!
> > > > >
> > > > > "If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. "
> > > > > No, you haven't. You have shown that real numbers with a finite representation are countable. One third is not on your list, John. Try again.. Think better next time.
> > > > It's too bad that you are butt-hurt because you thought you understood, but the fact is that you shouldn't be trying to do any mathematics. You're simply inept.
> > > Which index does 1/3 correspond to?
> > On what tree branch is 0.333...., you fucking moron?!!!!!
> >
> > You agreed with Mark Chu Carroll that 0.333... is in my tree. On what level is it, you little pisshead????!?!!!!
> Sure, it is in the tree but it doesn't correspond to a natural number.

Doesn't have to. It has a unique name according to mainstream which is 0.333...
Therefore, since all the elements have unique names AND can be systematically names R is countable contrary to your crank father Cantor.

>
> I don't know who Chu Carroll is, but a Google search revealed he's a math professor.

Nothing of the sort. He has a computer science degree.

> Have you had a discussion with him and he also brought up this point? Yes, in that case I think we agree.

torsdag 31 augusti 2023 kl. 17:17:26 UTC+2 skrev Eram semper recta:
> On Thursday, 31 August 2023 at 06:24:02 UTC-4, mark
> > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > 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.
> > > > > > > > > > > > > > > > > > I have to agree, but this is a persistent problem with John. He does not use the usual definitions in math, and usually invents his own (non-working definitions). Let me give me a couple of examples:
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > 1. when discussing countability, he invents his own (quite vague definition) and then claims victory whenever the other person does not use the same definition.
> > > > > > > > > > > > > > > > > You little bastard! Enjoy lying again?
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > I said: A set is countable if and only if, its members can be systematically assigned unique names.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > That is exactly the correct definition. The one you are taught about one-to-one with N is due to the fact that you are too stupid to understand the correct definition. One-to-one with N works because N is countable and N is countable because its elements can be systematically assigned unique names.
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > <Your drivel is ignored>
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > Try to stop being the little cunt that you are and lying about what I said and did not say, you vile little bastard!
> > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > DIE QUICKLY!!!
> > > > > > > > > > > > > > > > What does it mean to "systematically assigned unique names"? Injection into N?
> > > > > > > > > > > > > > > Dumb fuckwad!
> > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
> > > > > > > > > > > > > > https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
> > > > > > > > > > > > > What does it mean to "index" a set, in your own words?
> > > > > > > > > > > > Study the article, you retard! The answer is there 'in my words', moron!
> > > > > > > > > > > The fucking imbecile Klyver doesn't realise that a one-to-one correspondence with N is the same as indexing. It takes genius to realise that indexing is just another way of systematically naming elements of another set.
> > > > > > > > > > >
> > > > > > > > > > > You can't fix stupid!
> > > > > > > > > > If you use the same definition, then R isn't countable.
> > > > > > > > > That's what I have been telling you, idiot! PAY ATTENTION..
> > > > > > > > >
> > > > > > > > > R is not countable because its elements cannot be systematically named.
> > > > > > > > >
> > > > > > > > > N is countable because its elements can be systematically named. That is why Cantor chose N as index set.
> > > > > > > > >
> > > > > > > > > Think moron, think.
> > > > > > > > If you use the mainstream definition, then R is not countable contrary to your claim.
> > > > > > > If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. However, contrary to your lies about me having made a claim that R is countable, I have shown that R is not countable by using the correct definition:
> > > > > > >
> > > > > > > A set is countable if and only if, it's members can be systematically named (each name must be unique).
> > > > > > >
> > > > > > > And this is why N is countable, because it conforms to the above definition.
> > > > > > >
> > > > > > > DIE QUICKLY! You moronic piece of shit!!!
> > > > > >
> > > > > > "If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. "
> > > > > > No, you haven't. You have shown that real numbers with a finite representation are countable. One third is not on your list, John. Try again. Think better next time.
> > > > > It's too bad that you are butt-hurt because you thought you understood, but the fact is that you shouldn't be trying to do any mathematics. You're simply inept.
> > > > Which index does 1/3 correspond to?
> > > On what tree branch is 0.333...., you fucking moron?!!!!!
> > >
> > > You agreed with Mark Chu Carroll that 0.333... is in my tree. On what level is it, you little pisshead????!?!!!!
> > Sure, it is in the tree but it doesn't correspond to a natural number.
> Doesn't have to. It has a unique name according to mainstream which is 0.333...
> Therefore, since all the elements have unique names AND can be systematically names R is countable contrary to your crank father Cantor.
> >
> > I don't know who Chu Carroll is, but a Google search revealed he's a math professor.
> Nothing of the sort. He has a computer science degree.
> > Have you had a discussion with him and he also brought up this point? Yes, in that case I think we agree.
> If you did a search, then you would have known the answer, crank!
> >
> > But I don't know who it is and I haven't seen your discussion.
> >
> > I agree that 1/3 is in the tree (not as a node or course, but as an entire path). I do not agree you have a bijection. 1/3 doesn't correspond to any natural number.
> Like I said, it doesn't have to. For a set to be countable means its elements can be systematically named and that is why N is countable and R is not, that is, elements of R do not exist.

On Thursday, 31 August 2023 at 11:27:04 UTC-4, markus...@gmail.com wrote:
> torsdag 31 augusti 2023 kl. 17:17:26 UTC+2 skrev Eram semper recta:
> > On Thursday, 31 August 2023 at 06:24:02 UTC-4, mark
> > > > > > > > > > > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > > > > > > > > > > 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.
> > > > > > > > > > > > > > > > > > > I have to agree, but this is a persistent problem with John. He does not use the usual definitions in math, and usually invents his own (non-working definitions). Let me give me a couple of examples:
> > > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > > 1. when discussing countability, he invents his own (quite vague definition) and then claims victory whenever the other person does not use the same definition.
> > > > > > > > > > > > > > > > > > You little bastard! Enjoy lying again?
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > I said: A set is countable if and only if, its members can be systematically assigned unique names.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > That is exactly the correct definition. The one you are taught about one-to-one with N is due to the fact that you are too stupid to understand the correct definition. One-to-one with N works because N is countable and N is countable because its elements can be systematically assigned unique names.
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > <Your drivel is ignored>
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > Try to stop being the little cunt that you are and lying about what I said and did not say, you vile little bastard!
> > > > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > > > DIE QUICKLY!!!
> > > > > > > > > > > > > > > > > What does it mean to "systematically assigned unique names"? Injection into N?
> > > > > > > > > > > > > > > > Dumb fuckwad!
> > > > > > > > > > > > > > > >
> > > > > > > > > > > > > > > > https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
> > > > > > > > > > > > > > > https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
> > > > > > > > > > > > > > What does it mean to "index" a set, in your own words?
> > > > > > > > > > > > > Study the article, you retard! The answer is there 'in my words', moron!
> > > > > > > > > > > > The fucking imbecile Klyver doesn't realise that a one-to-one correspondence with N is the same as indexing. It takes genius to realise that indexing is just another way of systematically naming elements of another set.
> > > > > > > > > > > >
> > > > > > > > > > > > You can't fix stupid!
> > > > > > > > > > > If you use the same definition, then R isn't countable.
> > > > > > > > > > That's what I have been telling you, idiot! PAY ATTENTION.
> > > > > > > > > >
> > > > > > > > > > R is not countable because its elements cannot be systematically named.
> > > > > > > > > >
> > > > > > > > > > N is countable because its elements can be systematically named. That is why Cantor chose N as index set.
> > > > > > > > > >
> > > > > > > > > > Think moron, think.
> > > > > > > > > If you use the mainstream definition, then R is not countable contrary to your claim.
> > > > > > > > If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. However, contrary to your lies about me having made a claim that R is countable, I have shown that R is not countable by using the correct definition:
> > > > > > > >
> > > > > > > > A set is countable if and only if, it's members can be systematically named (each name must be unique).
> > > > > > > >
> > > > > > > > And this is why N is countable, because it conforms to the above definition.
> > > > > > > >
> > > > > > > > DIE QUICKLY! You moronic piece of shit!!!
> > > > > > >
> > > > > > > "If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. "
> > > > > > > No, you haven't. You have shown that real numbers with a finite representation are countable. One third is not on your list, John. Try again. Think better next time.
> > > > > > It's too bad that you are butt-hurt because you thought you understood, but the fact is that you shouldn't be trying to do any mathematics.. You're simply inept.
> > > > > Which index does 1/3 correspond to?
> > > > On what tree branch is 0.333...., you fucking moron?!!!!!
> > > >
> > > > You agreed with Mark Chu Carroll that 0.333... is in my tree. On what level is it, you little pisshead????!?!!!!
> > > Sure, it is in the tree but it doesn't correspond to a natural number..
> > Doesn't have to. It has a unique name according to mainstream which is 0.333...
> > Therefore, since all the elements have unique names AND can be systematically names R is countable contrary to your crank father Cantor.
> > >
> > > I don't know who Chu Carroll is, but a Google search revealed he's a math professor.
> > Nothing of the sort. He has a computer science degree.
> > > Have you had a discussion with him and he also brought up this point? Yes, in that case I think we agree.
> > If you did a search, then you would have known the answer, crank!
> > >
> > > But I don't know who it is and I haven't seen your discussion.
> > >
> > > I agree that 1/3 is in the tree (not as a node or course, but as an entire path). I do not agree you have a bijection. 1/3 doesn't correspond to any natural number.
> > Like I said, it doesn't have to. For a set to be countable means its elements can be systematically named and that is why N is countable and R is not, that is, elements of R do not exist.
> As I said, I have no idea who he is. Google gave me a math professor and a software developer at Spotify. No computer scientist. So idk.
>
> Either way, he is not relevant here. 1/3 has to correspond to an index, by your own definition. There is no index for 1/3, hence you haven't shown R is countable.
>
> If it doesn't have to correspond to an index, then what do you mean by "countable"?

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

Mainstream cranks never ask themselves why N is countable.

A set is countable if and only if, its members can be systematically named.

Indexing (1-1 with N) is just one way of naming the elements.

One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.

Mainstream math cranks do not understand.

The only crank here is you. YOU do not understand squat of Mathematics. Just 🎲 already!

On Thursday, August 31, 2023 at 12:01:22 PM 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
>
> Mainstream cranks never ask themselves why N is countable.
>
> A set is countable if and only if, its members can be systematically named.
>
> Indexing (1-1 with N) is just one way of naming the elements.
>
> One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
>
> Mainstream math cranks do not understand.

On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
>
> Mainstream cranks never ask themselves why N is countable.
>
> A set is countable if and only if, its members can be systematically named.
>
> Indexing (1-1 with N) is just one way of naming the elements.
>
> One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
>
> Mainstream math cranks do not understand.

Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?
That countability means bijection with the natural numbers because everybody (except you) say it is.
You don't get to call others wrong by making up your own definition.

On 8/30/2023 4:23 PM, markus...@gmail.com wrote:
> torsdag 31 augusti 2023 kl. 00:46:18 UTC+2 skrev Eram semper recta:
>> On Wednesday, 30 August 2023 at 11:07:15 UTC-4, markus...@
>>>>>>>>>>>>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>>>> I have to agree, but this is a persistent problem with John. He does not use the usual definitions in math, and usually invents his own (non-working definitions). Let me give me a couple of examples:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 1. when discussing countability, he invents his own (quite vague definition) and then claims victory whenever the other person does not use the same definition.
>>>>>>>>>>>>>> You little bastard! Enjoy lying again?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I said: A set is countable if and only if, its members can be systematically assigned unique names.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That is exactly the correct definition. The one you are taught about one-to-one with N is due to the fact that you are too stupid to understand the correct definition. One-to-one with N works because N is countable and N is countable because its elements can be systematically assigned unique names.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> <Your drivel is ignored>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Try to stop being the little cunt that you are and lying about what I said and did not say, you vile little bastard!
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> DIE QUICKLY!!!
>>>>>>>>>>>>> What does it mean to "systematically assigned unique names"? Injection into N?
>>>>>>>>>>>> Dumb fuckwad!
>>>>>>>>>>>>
>>>>>>>>>>>> https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
>>>>>>>>>>> https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
>>>>>>>>>> What does it mean to "index" a set, in your own words?
>>>>>>>>> Study the article, you retard! The answer is there 'in my words', moron!
>>>>>>>> The fucking imbecile Klyver doesn't realise that a one-to-one correspondence with N is the same as indexing. It takes genius to realise that indexing is just another way of systematically naming elements of another set.
>>>>>>>>
>>>>>>>> You can't fix stupid!
>>>>>>> If you use the same definition, then R isn't countable.
>>>>>> That's what I have been telling you, idiot! PAY ATTENTION.
>>>>>>
>>>>>> R is not countable because its elements cannot be systematically named.
>>>>>>
>>>>>> N is countable because its elements can be systematically named. That is why Cantor chose N as index set.
>>>>>>
>>>>>> Think moron, think.
>>>>> If you use the mainstream definition, then R is not countable contrary to your claim.
>>>> If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. However, contrary to your lies about me having made a claim that R is countable, I have shown that R is not countable by using the correct definition:
>>>>
>>>> A set is countable if and only if, it's members can be systematically named (each name must be unique).
>>>>
>>>> And this is why N is countable, because it conforms to the above definition.
>>>>
>>>> DIE QUICKLY! You moronic piece of shit!!!
>>>
>>> "If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. "
>>> No, you haven't. You have shown that real numbers with a finite representation are countable. One third is not on your list, John. Try again. Think better next time.
>> It's too bad that you are butt-hurt because you thought you understood, but the fact is that you shouldn't be trying to do any mathematics. You're simply inept.
>
> Which index does 1/3 correspond to?

Depends on the scale and resolution. ;^)

i[0] = 0
i[1] = 1/6
i[2] = 1/3
....

So, 1/3 is index i[2].

i[0] = 0
i[1] = 1/12
i[2] = 1/6
i[3] = 1/3
....

1/3 is index i[3] here.

torsdag 31 augusti 2023 kl. 18:01:22 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
>
> Mainstream cranks never ask themselves why N is countable.
>
> A set is countable if and only if, its members can be systematically named.
>
> Indexing (1-1 with N) is just one way of naming the elements.
>
> One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
>
> Mainstream math cranks do not understand.

Where are you getting this definition from? Is 1-1 correspondence is only an example of "indexing elements", what is the general definition of "indexing a set" then? How do we know if a set can be indexed or not?

On 8/31/2023 3:23 AM, markus...@gmail.com wrote:
> torsdag 31 augusti 2023 kl. 11:56:37 UTC+2 skrev Eram semper recta:
>> On Wednesday, 30 August 2023 at 19:23:58 UTC-4, markus> > > > > > > > > > > > > > > > > > > > > > > > > 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.
>>>>>>>>>>>>>>>>> I have to agree, but this is a persistent problem with John. He does not use the usual definitions in math, and usually invents his own (non-working definitions). Let me give me a couple of examples:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> 1. when discussing countability, he invents his own (quite vague definition) and then claims victory whenever the other person does not use the same definition.
>>>>>>>>>>>>>>>> You little bastard! Enjoy lying again?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I said: A set is countable if and only if, its members can be systematically assigned unique names.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> That is exactly the correct definition. The one you are taught about one-to-one with N is due to the fact that you are too stupid to understand the correct definition. One-to-one with N works because N is countable and N is countable because its elements can be systematically assigned unique names.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> <Your drivel is ignored>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Try to stop being the little cunt that you are and lying about what I said and did not say, you vile little bastard!
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> DIE QUICKLY!!!
>>>>>>>>>>>>>>> What does it mean to "systematically assigned unique names"? Injection into N?
>>>>>>>>>>>>>> Dumb fuckwad!
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
>>>>>>>>>>>>> https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
>>>>>>>>>>>> What does it mean to "index" a set, in your own words?
>>>>>>>>>>> Study the article, you retard! The answer is there 'in my words', moron!
>>>>>>>>>> The fucking imbecile Klyver doesn't realise that a one-to-one correspondence with N is the same as indexing. It takes genius to realise that indexing is just another way of systematically naming elements of another set.
>>>>>>>>>>
>>>>>>>>>> You can't fix stupid!
>>>>>>>>> If you use the same definition, then R isn't countable.
>>>>>>>> That's what I have been telling you, idiot! PAY ATTENTION.
>>>>>>>>
>>>>>>>> R is not countable because its elements cannot be systematically named.
>>>>>>>>
>>>>>>>> N is countable because its elements can be systematically named. That is why Cantor chose N as index set.
>>>>>>>>
>>>>>>>> Think moron, think.
>>>>>>> If you use the mainstream definition, then R is not countable contrary to your claim.
>>>>>> If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. However, contrary to your lies about me having made a claim that R is countable, I have shown that R is not countable by using the correct definition:
>>>>>>
>>>>>> A set is countable if and only if, it's members can be systematically named (each name must be unique).
>>>>>>
>>>>>> And this is why N is countable, because it conforms to the above definition.
>>>>>>
>>>>>> DIE QUICKLY! You moronic piece of shit!!!
>>>>>
>>>>> "If you use the mainstream definition whereby it is incorrectly believed that real numbers can be expressed as "infinite decimal expansions" then R is indeed countable. "
>>>>> No, you haven't. You have shown that real numbers with a finite representation are countable. One third is not on your list, John. Try again. Think better next time.
>>>> It's too bad that you are butt-hurt because you thought you understood, but the fact is that you shouldn't be trying to do any mathematics. You're simply inept.
>>> Which index does 1/3 correspond to?
>> On what tree branch is 0.333...., you fucking moron?!!!!!
>>
>> You agreed with Mark Chu Carroll that 0.333... is in my tree. On what level is it, you little pisshead????!?!!!!
>
> Sure, it is in the tree but it doesn't correspond to a natural number.

A 3-ary tree:

0
/|\
/ | \
/ | \
1 2 3
................

It is build with natural numbers.

1
/|\
/ | \
/ | \
4 5 6
...............

So, trees are always interesting to me, well, they are fractal as
well... :^)

On 8/31/2023 1:19 PM, Chris M. Thomasson wrote:
> On 8/31/2023 3:23 AM, markus...@gmail.com wrote:
>> torsdag 31 augusti 2023 kl. 11:56:37 UTC+2 skrev Eram semper recta:
>>> On Wednesday, 30 August 2023 at 19:23:58 UTC-4, markus> > > > > > > >
>>> > > > > > > > > > > > > > > > > >
>>> 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.
>>>>>>>>>>>>>>>>>> I have to agree, but this is a persistent problem with
>>>>>>>>>>>>>>>>>> John. He does not use the usual definitions in math,
>>>>>>>>>>>>>>>>>> and usually invents his own (non-working definitions).
>>>>>>>>>>>>>>>>>> Let me give me a couple of examples:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> 1. when discussing countability, he invents his own
>>>>>>>>>>>>>>>>>> (quite vague definition) and then claims victory
>>>>>>>>>>>>>>>>>> whenever the other person does not use the same
>>>>>>>>>>>>>>>>>> definition.
>>>>>>>>>>>>>>>>> You little bastard! Enjoy lying again?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I said: A set is countable if and only if, its members
>>>>>>>>>>>>>>>>> can be systematically assigned unique names.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> That is exactly the correct definition. The one you are
>>>>>>>>>>>>>>>>> taught about one-to-one with N is due to the fact that
>>>>>>>>>>>>>>>>> you are too stupid to understand the correct
>>>>>>>>>>>>>>>>> definition. One-to-one with N works because N is
>>>>>>>>>>>>>>>>> countable and N is countable because its elements can
>>>>>>>>>>>>>>>>> be systematically assigned unique names.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> <Your drivel is ignored>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Try to stop being the little cunt that you are and
>>>>>>>>>>>>>>>>> lying about what I said and did not say, you vile
>>>>>>>>>>>>>>>>> little bastard!
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> DIE QUICKLY!!!
>>>>>>>>>>>>>>>> What does it mean to "systematically assigned unique
>>>>>>>>>>>>>>>> names"? Injection into N?
>>>>>>>>>>>>>>> Dumb fuckwad!
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
>>>>>>>>>>>>>> https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
>>>>>>>>>>>>> What does it mean to "index" a set, in your own words?
>>>>>>>>>>>> Study the article, you retard! The answer is there 'in my
>>>>>>>>>>>> words', moron!
>>>>>>>>>>> The fucking imbecile Klyver doesn't realise that a one-to-one
>>>>>>>>>>> correspondence with N is the same as indexing. It takes
>>>>>>>>>>> genius to realise that indexing is just another way of
>>>>>>>>>>> systematically naming elements of another set.
>>>>>>>>>>>
>>>>>>>>>>> You can't fix stupid!
>>>>>>>>>> If you use the same definition, then R isn't countable.
>>>>>>>>> That's what I have been telling you, idiot! PAY ATTENTION.
>>>>>>>>>
>>>>>>>>> R is not countable because its elements cannot be
>>>>>>>>> systematically named.
>>>>>>>>>
>>>>>>>>> N is countable because its elements can be systematically
>>>>>>>>> named. That is why Cantor chose N as index set.
>>>>>>>>>
>>>>>>>>> Think moron, think.
>>>>>>>> If you use the mainstream definition, then R is not countable
>>>>>>>> contrary to your claim.
>>>>>>> If you use the mainstream definition whereby it is incorrectly
>>>>>>> believed that real numbers can be expressed as "infinite decimal
>>>>>>> expansions" then R is indeed countable. However, contrary to your
>>>>>>> lies about me having made a claim that R is countable, I have
>>>>>>> shown that R is not countable by using the correct definition:
>>>>>>>
>>>>>>> A set is countable if and only if, it's members can be
>>>>>>> systematically named (each name must be unique).
>>>>>>>
>>>>>>> And this is why N is countable, because it conforms to the above
>>>>>>> definition.
>>>>>>>
>>>>>>> DIE QUICKLY! You moronic piece of shit!!!
>>>>>>
>>>>>> "If you use the mainstream definition whereby it is incorrectly
>>>>>> believed that real numbers can be expressed as "infinite decimal
>>>>>> expansions" then R is indeed countable. "
>>>>>> No, you haven't. You have shown that real numbers with a finite
>>>>>> representation are countable. One third is not on your list, John.
>>>>>> Try again. Think better next time.
>>>>> It's too bad that you are butt-hurt because you thought you
>>>>> understood, but the fact is that you shouldn't be trying to do any
>>>>> mathematics. You're simply inept.
>>>> Which index does 1/3 correspond to?
>>> On what tree branch is 0.333...., you fucking moron?!!!!!
>>>
>>> You agreed with Mark Chu Carroll that 0.333... is in my tree. On what
>>> level is it, you little pisshead????!?!!!!
>>
>> Sure, it is in the tree but it doesn't correspond to a natural number.
>
> A 3-ary tree:
>
>      0
>     /|\
>    / | \
>   /  |  \
>  1   2   3
> ...............
>
>
> It is build with natural numbers.
>
>      1
>     /|\
>    / | \
>   /  |  \
>  4   5   6
> ..............
>
> So, trees are always interesting to me, well, they are fractal as
> well... :^)
>
>

On 8/31/2023 1:19 PM, Chris M. Thomasson wrote:
> On 8/31/2023 3:23 AM, markus...@gmail.com wrote:
>> torsdag 31 augusti 2023 kl. 11:56:37 UTC+2 skrev Eram semper recta:
>>> On Wednesday, 30 August 2023 at 19:23:58 UTC-4, markus> > > > > > > >
>>> > > > > > > > > > > > > > > > > >
>>> 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.
>>>>>>>>>>>>>>>>>> I have to agree, but this is a persistent problem with
>>>>>>>>>>>>>>>>>> John. He does not use the usual definitions in math,
>>>>>>>>>>>>>>>>>> and usually invents his own (non-working definitions).
>>>>>>>>>>>>>>>>>> Let me give me a couple of examples:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> 1. when discussing countability, he invents his own
>>>>>>>>>>>>>>>>>> (quite vague definition) and then claims victory
>>>>>>>>>>>>>>>>>> whenever the other person does not use the same
>>>>>>>>>>>>>>>>>> definition.
>>>>>>>>>>>>>>>>> You little bastard! Enjoy lying again?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I said: A set is countable if and only if, its members
>>>>>>>>>>>>>>>>> can be systematically assigned unique names.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> That is exactly the correct definition. The one you are
>>>>>>>>>>>>>>>>> taught about one-to-one with N is due to the fact that
>>>>>>>>>>>>>>>>> you are too stupid to understand the correct
>>>>>>>>>>>>>>>>> definition. One-to-one with N works because N is
>>>>>>>>>>>>>>>>> countable and N is countable because its elements can
>>>>>>>>>>>>>>>>> be systematically assigned unique names.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> <Your drivel is ignored>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Try to stop being the little cunt that you are and
>>>>>>>>>>>>>>>>> lying about what I said and did not say, you vile
>>>>>>>>>>>>>>>>> little bastard!
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> DIE QUICKLY!!!
>>>>>>>>>>>>>>>> What does it mean to "systematically assigned unique
>>>>>>>>>>>>>>>> names"? Injection into N?
>>>>>>>>>>>>>>> Dumb fuckwad!
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
>>>>>>>>>>>>>> https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
>>>>>>>>>>>>> What does it mean to "index" a set, in your own words?
>>>>>>>>>>>> Study the article, you retard! The answer is there 'in my
>>>>>>>>>>>> words', moron!
>>>>>>>>>>> The fucking imbecile Klyver doesn't realise that a one-to-one
>>>>>>>>>>> correspondence with N is the same as indexing. It takes
>>>>>>>>>>> genius to realise that indexing is just another way of
>>>>>>>>>>> systematically naming elements of another set.
>>>>>>>>>>>
>>>>>>>>>>> You can't fix stupid!
>>>>>>>>>> If you use the same definition, then R isn't countable.
>>>>>>>>> That's what I have been telling you, idiot! PAY ATTENTION.
>>>>>>>>>
>>>>>>>>> R is not countable because its elements cannot be
>>>>>>>>> systematically named.
>>>>>>>>>
>>>>>>>>> N is countable because its elements can be systematically
>>>>>>>>> named. That is why Cantor chose N as index set.
>>>>>>>>>
>>>>>>>>> Think moron, think.
>>>>>>>> If you use the mainstream definition, then R is not countable
>>>>>>>> contrary to your claim.
>>>>>>> If you use the mainstream definition whereby it is incorrectly
>>>>>>> believed that real numbers can be expressed as "infinite decimal
>>>>>>> expansions" then R is indeed countable. However, contrary to your
>>>>>>> lies about me having made a claim that R is countable, I have
>>>>>>> shown that R is not countable by using the correct definition:
>>>>>>>
>>>>>>> A set is countable if and only if, it's members can be
>>>>>>> systematically named (each name must be unique).
>>>>>>>
>>>>>>> And this is why N is countable, because it conforms to the above
>>>>>>> definition.
>>>>>>>
>>>>>>> DIE QUICKLY! You moronic piece of shit!!!
>>>>>>
>>>>>> "If you use the mainstream definition whereby it is incorrectly
>>>>>> believed that real numbers can be expressed as "infinite decimal
>>>>>> expansions" then R is indeed countable. "
>>>>>> No, you haven't. You have shown that real numbers with a finite
>>>>>> representation are countable. One third is not on your list, John.
>>>>>> Try again. Think better next time.
>>>>> It's too bad that you are butt-hurt because you thought you
>>>>> understood, but the fact is that you shouldn't be trying to do any
>>>>> mathematics. You're simply inept.
>>>> Which index does 1/3 correspond to?
>>> On what tree branch is 0.333...., you fucking moron?!!!!!
>>>
>>> You agreed with Mark Chu Carroll that 0.333... is in my tree. On what
>>> level is it, you little pisshead????!?!!!!
>>
>> Sure, it is in the tree but it doesn't correspond to a natural number.
>
> A 3-ary tree:
[...]

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

>> So, trees are always interesting to me,

I draw your attention to the Calkin-Wilf tree and the Sterne-Brocot
tree. Both beautiful ways to enumerate the (positive) rationals:

https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree
https://en.wikipedia.org/wiki/Stern%E2%80%93Brocot_tree

--
Ben.

torsdag 31 augusti 2023 kl. 23:21:18 UTC+2 skrev Ben Bacarisse:
> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>
> >> So, trees are always interesting to me,
> I draw your attention to the Calkin-Wilf tree and the Sterne-Brocot
> tree. Both beautiful ways to enumerate the (positive) rationals:
>
> https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree
> https://en.wikipedia.org/wiki/Stern%E2%80%93Brocot_tree
>
> --
> Ben.
Yes, the rationals are countable but John claims he can prove the reals are countable.

On 8/31/2023 1:24 PM, Chris M. Thomasson wrote:
> On 8/31/2023 1:19 PM, Chris M. Thomasson wrote:
>> On 8/31/2023 3:23 AM, markus...@gmail.com wrote:
>>> torsdag 31 augusti 2023 kl. 11:56:37 UTC+2 skrev Eram semper recta:
>>>> On Wednesday, 30 August 2023 at 19:23:58 UTC-4, markus> > > > > > >
>>>> > > > > > > > > > > > > > > > > > >
>>>> 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.
>>>>>>>>>>>>>>>>>>> I have to agree, but this is a persistent problem
>>>>>>>>>>>>>>>>>>> with John. He does not use the usual definitions in
>>>>>>>>>>>>>>>>>>> math, and usually invents his own (non-working
>>>>>>>>>>>>>>>>>>> definitions). Let me give me a couple of examples:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> 1. when discussing countability, he invents his own
>>>>>>>>>>>>>>>>>>> (quite vague definition) and then claims victory
>>>>>>>>>>>>>>>>>>> whenever the other person does not use the same
>>>>>>>>>>>>>>>>>>> definition.
>>>>>>>>>>>>>>>>>> You little bastard! Enjoy lying again?
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I said: A set is countable if and only if, its members
>>>>>>>>>>>>>>>>>> can be systematically assigned unique names.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> That is exactly the correct definition. The one you
>>>>>>>>>>>>>>>>>> are taught about one-to-one with N is due to the fact
>>>>>>>>>>>>>>>>>> that you are too stupid to understand the correct
>>>>>>>>>>>>>>>>>> definition. One-to-one with N works because N is
>>>>>>>>>>>>>>>>>> countable and N is countable because its elements can
>>>>>>>>>>>>>>>>>> be systematically assigned unique names.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> <Your drivel is ignored>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Try to stop being the little cunt that you are and
>>>>>>>>>>>>>>>>>> lying about what I said and did not say, you vile
>>>>>>>>>>>>>>>>>> little bastard!
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> DIE QUICKLY!!!
>>>>>>>>>>>>>>>>> What does it mean to "systematically assigned unique
>>>>>>>>>>>>>>>>> names"? Injection into N?
>>>>>>>>>>>>>>>> Dumb fuckwad!
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> https://groups.google.com/g/sci.math/c/MaE0LgrMB9g/m/M0_Slvw0BwAJ
>>>>>>>>>>>>>>> https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks
>>>>>>>>>>>>>> What does it mean to "index" a set, in your own words?
>>>>>>>>>>>>> Study the article, you retard! The answer is there 'in my
>>>>>>>>>>>>> words', moron!
>>>>>>>>>>>> The fucking imbecile Klyver doesn't realise that a
>>>>>>>>>>>> one-to-one correspondence with N is the same as indexing. It
>>>>>>>>>>>> takes genius to realise that indexing is just another way of
>>>>>>>>>>>> systematically naming elements of another set.
>>>>>>>>>>>>
>>>>>>>>>>>> You can't fix stupid!
>>>>>>>>>>> If you use the same definition, then R isn't countable.
>>>>>>>>>> That's what I have been telling you, idiot! PAY ATTENTION.
>>>>>>>>>>
>>>>>>>>>> R is not countable because its elements cannot be
>>>>>>>>>> systematically named.
>>>>>>>>>>
>>>>>>>>>> N is countable because its elements can be systematically
>>>>>>>>>> named. That is why Cantor chose N as index set.
>>>>>>>>>>
>>>>>>>>>> Think moron, think.
>>>>>>>>> If you use the mainstream definition, then R is not countable
>>>>>>>>> contrary to your claim.
>>>>>>>> If you use the mainstream definition whereby it is incorrectly
>>>>>>>> believed that real numbers can be expressed as "infinite decimal
>>>>>>>> expansions" then R is indeed countable. However, contrary to
>>>>>>>> your lies about me having made a claim that R is countable, I
>>>>>>>> have shown that R is not countable by using the correct definition:
>>>>>>>>
>>>>>>>> A set is countable if and only if, it's members can be
>>>>>>>> systematically named (each name must be unique).
>>>>>>>>
>>>>>>>> And this is why N is countable, because it conforms to the above
>>>>>>>> definition.
>>>>>>>>
>>>>>>>> DIE QUICKLY! You moronic piece of shit!!!
>>>>>>>
>>>>>>> "If you use the mainstream definition whereby it is incorrectly
>>>>>>> believed that real numbers can be expressed as "infinite decimal
>>>>>>> expansions" then R is indeed countable. "
>>>>>>> No, you haven't. You have shown that real numbers with a finite
>>>>>>> representation are countable. One third is not on your list,
>>>>>>> John. Try again. Think better next time.
>>>>>> It's too bad that you are butt-hurt because you thought you
>>>>>> understood, but the fact is that you shouldn't be trying to do any
>>>>>> mathematics. You're simply inept.
>>>>> Which index does 1/3 correspond to?
>>>> On what tree branch is 0.333...., you fucking moron?!!!!!
>>>>
>>>> You agreed with Mark Chu Carroll that 0.333... is in my tree. On
>>>> what level is it, you little pisshead????!?!!!!
>>>
>>> Sure, it is in the tree but it doesn't correspond to a natural number.
>>
>> A 3-ary tree:
> [...]
>
> Trees are fun!
>
>  ..............
>   -3  -2  -1
>     \  |  /
>      \ | /
>       \|/
>        0
>       /|\
>      / | \
>     /  |  \
>    1   2   3
>  ..............
>
> :^D
>

markus...@gmail.com explained on 8/31/2023 :
> torsdag 31 augusti 2023 kl. 23:21:18 UTC+2 skrev Ben Bacarisse:
>> "Chris M. Thomasson" <chris.m.t...@gmail.com> writes:
>>
>>>> So, trees are always interesting to me,
>> I draw your attention to the Calkin-Wilf tree and the Sterne-Brocot
>> tree. Both beautiful ways to enumerate the (positive) rationals:
>>
>> https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree
>> https://en.wikipedia.org/wiki/Stern%E2%80%93Brocot_tree
>>
>> --
>> Ben.
> Yes, the rationals are countable but John claims he can prove the reals are
> countable.

John claims lots of things, most here simply ignore him.

On Thursday, 31 August 2023 at 15:05:30 UTC-4, Kevin S wrote:
> On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
> >
> > Mainstream cranks never ask themselves why N is countable.
> >
> > A set is countable if and only if, its members can be systematically named.
> >
> > Indexing (1-1 with N) is just one way of naming the elements.
> >
> > One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
> >
> > Mainstream math cranks do not understand.
> Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?

That is what countability means. Initially it was defined as follows:

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

Ever ask yourself why N is countable and why a bijection with N is used?

Answer: The elements of N can be systematically named using any radix system.

> That countability means bijection with the natural numbers because everybody (except you) say it is.

No. Bijection with N is one way of checking for countability, but not the essence of what it means.

> You don't get to call others wrong by making up your own definition.

I do call them wrong because they are WRONG. And no, I didn't make up that definition. It is the original Cantor definition.

On Friday, 1 September 2023 at 11:14:00 UTC-4, Eram semper recta wrote:
> On Thursday, 31 August 2023 at 15:05:30 UTC-4, Kevin S wrote:
> > On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
> > >
> > > Mainstream cranks never ask themselves why N is countable.
> > >
> > > A set is countable if and only if, its members can be systematically named.
> > >
> > > Indexing (1-1 with N) is just one way of naming the elements.
> > >
> > > One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
> > >
> > > Mainstream math cranks do not understand.
> > Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?
> That is what countability means. Initially it was defined as follows:
>
> A set is countable if and only if, its members can be listed.
>
> Ever ask yourself why N is countable and why a bijection with N is used?
>
> Answer: The elements of N can be systematically named using any radix system.
> > That countability means bijection with the natural numbers because everybody (except you) say it is.
> No. Bijection with N is one way of checking for countability, but not the essence of what it means.
> > You don't get to call others wrong by making up your own definition.
> I do call them wrong because they are WRONG. And no, I didn't make up that definition. It is the original Cantor definition.

In mathematics, a set is said to be countable if its elements can be "numbered" using the natural numbers. More precisely (meaning for imbeciles who are not geniuses like John Gabriel), this means that there exists a one-to-one mapping from this set to (not necessarily onto) the set of natural numbers.

John Gabriel knows that elements being numbered is the same as being INDEXED or given a UNIQUE NAME. Learn from me, you syphilitic, stupid, jealous bastards!!!

Your moronic math professors and teachers DO NOT know or understand these things. They are my intellectual inferiors as are YOU!

All of you are not worth one turd of mine.

On 8/31/2023 2:21 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>>> So, trees are always interesting to me,
>
> I draw your attention to the Calkin-Wilf tree and the Sterne-Brocot
> tree. Both beautiful ways to enumerate the (positive) rationals:
>
> https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree
> https://en.wikipedia.org/wiki/Stern%E2%80%93Brocot_tree
>

Nice heads up here Ben! Thanks.

fredag 1 september 2023 kl. 17:31:34 UTC+2 skrev Eram semper recta:
> On Friday, 1 September 2023 at 11:14:00 UTC-4, Eram semper recta wrote:
> > On Thursday, 31 August 2023 at 15:05:30 UTC-4, Kevin S wrote:
> > > On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
> > > >
> > > > Mainstream cranks never ask themselves why N is countable.
> > > >
> > > > A set is countable if and only if, its members can be systematically named.
> > > >
> > > > Indexing (1-1 with N) is just one way of naming the elements.
> > > >
> > > > One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
> > > >
> > > > Mainstream math cranks do not understand.
> > > Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?
> > That is what countability means. Initially it was defined as follows:
> >
> > A set is countable if and only if, its members can be listed.
> >
> > Ever ask yourself why N is countable and why a bijection with N is used?
> >
> > Answer: The elements of N can be systematically named using any radix system.
> > > That countability means bijection with the natural numbers because everybody (except you) say it is.
> > No. Bijection with N is one way of checking for countability, but not the essence of what it means.
> > > You don't get to call others wrong by making up your own definition.
> > I do call them wrong because they are WRONG. And no, I didn't make up that definition. It is the original Cantor definition.
> In mathematics, a set is said to be countable if its elements can be "numbered" using the natural numbers. More precisely (meaning for imbeciles who are not geniuses like John Gabriel), this means that there exists a one-to-one mapping from this set to (not necessarily onto) the set of natural numbers.
>
> John Gabriel knows that elements being numbered is the same as being INDEXED or given a UNIQUE NAME. Learn from me, you syphilitic, stupid, jealous bastards!!!
>
>
> Your moronic math professors and teachers DO NOT know or understand these things. They are my intellectual inferiors as are YOU!
>
>
> All of you are not worth one turd of mine.
What does it mean to index a set?
what is the general definition of "indexing a set" then? How do we know if a set can be indexed or not?

On Friday, 1 September 2023 at 16:51:49 UTC-4, markus...@gmail.com wrote:
> fredag 1 september 2023 kl. 17:31:34 UTC+2 skrev Eram semper recta:
> > On Friday, 1 September 2023 at 11:14:00 UTC-4, Eram semper recta wrote:
> > > On Thursday, 31 August 2023 at 15:05:30 UTC-4, Kevin S wrote:
> > > > On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
> > > > >
> > > > > Mainstream cranks never ask themselves why N is countable.
> > > > >
> > > > > A set is countable if and only if, its members can be systematically named.
> > > > >
> > > > > Indexing (1-1 with N) is just one way of naming the elements.
> > > > >
> > > > > One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
> > > > >
> > > > > Mainstream math cranks do not understand.
> > > > Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?
> > > That is what countability means. Initially it was defined as follows:
> > >
> > > A set is countable if and only if, its members can be listed.
> > >
> > > Ever ask yourself why N is countable and why a bijection with N is used?
> > >
> > > Answer: The elements of N can be systematically named using any radix system.
> > > > That countability means bijection with the natural numbers because everybody (except you) say it is.
> > > No. Bijection with N is one way of checking for countability, but not the essence of what it means.
> > > > You don't get to call others wrong by making up your own definition..
> > > I do call them wrong because they are WRONG. And no, I didn't make up that definition. It is the original Cantor definition.
> > In mathematics, a set is said to be countable if its elements can be "numbered" using the natural numbers. More precisely (meaning for imbeciles who are not geniuses like John Gabriel), this means that there exists a one-to-one mapping from this set to (not necessarily onto) the set of natural numbers.
> >
> > John Gabriel knows that elements being numbered is the same as being INDEXED or given a UNIQUE NAME. Learn from me, you syphilitic, stupid, jealous bastards!!!
> >
> >
> > Your moronic math professors and teachers DO NOT know or understand these things. They are my intellectual inferiors as are YOU!
> >
> >
> > All of you are not worth one turd of mine.
> What does it mean to index a set?

When you visit a library to find a particular book, do you not look it up in an index that tells you where that book is?

Gosh, you are one prize moron.

Here is a simpler example. Consider the set T={cars, airplanes, ships}. There are many types of cars and car dealers as there are airplanes and ships.

We could create an index that goes something like this:

1 - Toyota (1)
BMW (2)
Mercedes (3)
etc
2 - Mirage (1)
F16 (2)
Raptor (3)
etc
3 - Cruiser (1)
Frigate (2)
Submarine (3)
etc
Now we have a lot of information about all these forms of transport but not enough memory. So what do we do, we store the information using an index. For example, we can say Description 2(3): Speed: Mach 2 and so on.

In the same way, the father of all mainstream mathematical cranks such as yourself, realised that the set of Natural Numbers serves as a very good indexing tool.

The reason the mythical set R is not countable is due to the fact that R does not exist! In other words, you cannot NAME the elements of R so that a natural number can be used to INDEX them. DO YOU UNDERSTAND NOW, YOU FUCKING MORON?

> what is the general definition of "indexing a set" then? How do we know if a set can be indexed or not?

BLAAAAAA DOOBI DDAAAAA Blurb dirb da da di di dum "I am a stupid Jew" - Markus Klyver.

On Saturday, 2 September 2023 at 09:49:02 UTC-4, Eram semper recta wrote:
> On Friday, 1 September 2023 at 16:51:49 UTC-4, markus...@gmail.com wrote:
> > fredag 1 september 2023 kl. 17:31:34 UTC+2 skrev Eram semper recta:
> > > On Friday, 1 September 2023 at 11:14:00 UTC-4, Eram semper recta wrote:
> > > > On Thursday, 31 August 2023 at 15:05:30 UTC-4, Kevin S wrote:
> > > > > On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
> > > > > >
> > > > > > Mainstream cranks never ask themselves why N is countable.
> > > > > >
> > > > > > A set is countable if and only if, its members can be systematically named.
> > > > > >
> > > > > > Indexing (1-1 with N) is just one way of naming the elements.
> > > > > >
> > > > > > One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
> > > > > >
> > > > > > Mainstream math cranks do not understand.
> > > > > Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?
> > > > That is what countability means. Initially it was defined as follows:
> > > >
> > > > A set is countable if and only if, its members can be listed.
> > > >
> > > > Ever ask yourself why N is countable and why a bijection with N is used?
> > > >
> > > > Answer: The elements of N can be systematically named using any radix system.
> > > > > That countability means bijection with the natural numbers because everybody (except you) say it is.
> > > > No. Bijection with N is one way of checking for countability, but not the essence of what it means.
> > > > > You don't get to call others wrong by making up your own definition.
> > > > I do call them wrong because they are WRONG. And no, I didn't make up that definition. It is the original Cantor definition.
> > > In mathematics, a set is said to be countable if its elements can be "numbered" using the natural numbers. More precisely (meaning for imbeciles who are not geniuses like John Gabriel), this means that there exists a one-to-one mapping from this set to (not necessarily onto) the set of natural numbers.
> > >
> > > John Gabriel knows that elements being numbered is the same as being INDEXED or given a UNIQUE NAME. Learn from me, you syphilitic, stupid, jealous bastards!!!
> > >
> > >
> > > Your moronic math professors and teachers DO NOT know or understand these things. They are my intellectual inferiors as are YOU!
> > >
> > >
> > > All of you are not worth one turd of mine.
> > What does it mean to index a set?
> When you visit a library to find a particular book, do you not look it up in an index that tells you where that book is?
>
> Gosh, you are one prize moron.
>
> Here is a simpler example. Consider the set T={cars, airplanes, ships}. There are many types of cars and car dealers as there are airplanes and ships.
>
> We could create an index that goes something like this:
>
> 1 - Toyota (1)
> BMW (2)
> Mercedes (3)
> etc
> 2 - Mirage (1)
> F16 (2)
> Raptor (3)
> etc
> 3 - Cruiser (1)
> Frigate (2)
> Submarine (3)
> etc
> Now we have a lot of information about all these forms of transport but not enough memory. So what do we do, we store the information using an index.. For example, we can say Description 2(3): Speed: Mach 2 and so on.
>
> In the same way, the father of all mainstream mathematical cranks such as yourself, realised that the set of Natural Numbers serves as a very good indexing tool.
>
> The reason the mythical set R is not countable is due to the fact that R does not exist! In other words, you cannot NAME the elements of R so that a natural number can be used to INDEX them. DO YOU UNDERSTAND NOW, YOU FUCKING MORON?
> > what is the general definition of "indexing a set" then? How do we know if a set can be indexed or not?
> BLAAAAAA DOOBI DDAAAAA Blurb dirb da da di di dum "I am a stupid Jew" - Markus Klyver.

Oh wait, I forgot turd head Klyver might ask what is the set being indexed. Tsk, tsk. Here is a quiz for you, dipstick!

[A] The sets are cars, airplanes, ships
[B] Apples, oranges and turds
[C] Um, I DONNUH KNOW>>>>>>>>>

lördag 2 september 2023 kl. 15:49:02 UTC+2 skrev Eram semper recta:
> On Friday, 1 September 2023 at 16:51:49 UTC-4, markus...@gmail.com wrote:
> > fredag 1 september 2023 kl. 17:31:34 UTC+2 skrev Eram semper recta:
> > > On Friday, 1 September 2023 at 11:14:00 UTC-4, Eram semper recta wrote:
> > > > On Thursday, 31 August 2023 at 15:05:30 UTC-4, Kevin S wrote:
> > > > > On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
> > > > > >
> > > > > > Mainstream cranks never ask themselves why N is countable.
> > > > > >
> > > > > > A set is countable if and only if, its members can be systematically named.
> > > > > >
> > > > > > Indexing (1-1 with N) is just one way of naming the elements.
> > > > > >
> > > > > > One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
> > > > > >
> > > > > > Mainstream math cranks do not understand.
> > > > > Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?
> > > > That is what countability means. Initially it was defined as follows:
> > > >
> > > > A set is countable if and only if, its members can be listed.
> > > >
> > > > Ever ask yourself why N is countable and why a bijection with N is used?
> > > >
> > > > Answer: The elements of N can be systematically named using any radix system.
> > > > > That countability means bijection with the natural numbers because everybody (except you) say it is.
> > > > No. Bijection with N is one way of checking for countability, but not the essence of what it means.
> > > > > You don't get to call others wrong by making up your own definition.
> > > > I do call them wrong because they are WRONG. And no, I didn't make up that definition. It is the original Cantor definition.
> > > In mathematics, a set is said to be countable if its elements can be "numbered" using the natural numbers. More precisely (meaning for imbeciles who are not geniuses like John Gabriel), this means that there exists a one-to-one mapping from this set to (not necessarily onto) the set of natural numbers.
> > >
> > > John Gabriel knows that elements being numbered is the same as being INDEXED or given a UNIQUE NAME. Learn from me, you syphilitic, stupid, jealous bastards!!!
> > >
> > >
> > > Your moronic math professors and teachers DO NOT know or understand these things. They are my intellectual inferiors as are YOU!
> > >
> > >
> > > All of you are not worth one turd of mine.
> > What does it mean to index a set?
> When you visit a library to find a particular book, do you not look it up in an index that tells you where that book is?
>
> Gosh, you are one prize moron.
>
> Here is a simpler example. Consider the set T={cars, airplanes, ships}. There are many types of cars and car dealers as there are airplanes and ships.
>
> We could create an index that goes something like this:
>
> 1 - Toyota (1)
> BMW (2)
> Mercedes (3)
> etc
> 2 - Mirage (1)
> F16 (2)
> Raptor (3)
> etc
> 3 - Cruiser (1)
> Frigate (2)
> Submarine (3)
> etc
> Now we have a lot of information about all these forms of transport but not enough memory. So what do we do, we store the information using an index.. For example, we can say Description 2(3): Speed: Mach 2 and so on.
>
> In the same way, the father of all mainstream mathematical cranks such as yourself, realised that the set of Natural Numbers serves as a very good indexing tool.
>
> The reason the mythical set R is not countable is due to the fact that R does not exist! In other words, you cannot NAME the elements of R so that a natural number can be used to INDEX them. DO YOU UNDERSTAND NOW, YOU FUCKING MORON?
> > what is the general definition of "indexing a set" then? How do we know if a set can be indexed or not?
> BLAAAAAA DOOBI DDAAAAA Blurb dirb da da di di dum "I am a stupid Jew" - Markus Klyver.

The examples you give are examples of indexing with natural numbers. But you said those are not the only indexes. Then, what do you mean by an "index"? The mainstream definition of countable defines countibility as indexing with natural numbers. You can't just change the definitions just because you feel like it and expect everyone to know you're inventing your own math and terminology.

And stop hating Jews.

On Tuesday, 5 September 2023 at 03:33:29 UTC-4, markus...@gmail.com wrote:
> lördag 2 september 2023 kl. 15:49:02 UTC+2 skrev Eram semper recta:
> > On Friday, 1 September 2023 at 16:51:49 UTC-4, markus...@gmail.com wrote:
> > > fredag 1 september 2023 kl. 17:31:34 UTC+2 skrev Eram semper recta:
> > > > On Friday, 1 September 2023 at 11:14:00 UTC-4, Eram semper recta wrote:
> > > > > On Thursday, 31 August 2023 at 15:05:30 UTC-4, Kevin S wrote:
> > > > > > On Thursday, August 31, 2023 at 6:01:22 PM UTC+2, 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
> > > > > > >
> > > > > > > Mainstream cranks never ask themselves why N is countable.
> > > > > > >
> > > > > > > A set is countable if and only if, its members can be systematically named.
> > > > > > >
> > > > > > > Indexing (1-1 with N) is just one way of naming the elements.
> > > > > > >
> > > > > > > One DOES NOT need a 1-1 correspondence with N because this is only the case when elements are indexed, However, this is not what is meant by countable set.
> > > > > > >
> > > > > > > Mainstream math cranks do not understand.
> > > > > > Where did you get the definition "A set is countable if and only if, its members can be systematically named." from?
> > > > > That is what countability means. Initially it was defined as follows:
> > > > >
> > > > > A set is countable if and only if, its members can be listed.
> > > > >
> > > > > Ever ask yourself why N is countable and why a bijection with N is used?
> > > > >
> > > > > Answer: The elements of N can be systematically named using any radix system.
> > > > > > That countability means bijection with the natural numbers because everybody (except you) say it is.
> > > > > No. Bijection with N is one way of checking for countability, but not the essence of what it means.
> > > > > > You don't get to call others wrong by making up your own definition.
> > > > > I do call them wrong because they are WRONG. And no, I didn't make up that definition. It is the original Cantor definition.
> > > > In mathematics, a set is said to be countable if its elements can be "numbered" using the natural numbers. More precisely (meaning for imbeciles who are not geniuses like John Gabriel), this means that there exists a one-to-one mapping from this set to (not necessarily onto) the set of natural numbers.
> > > >
> > > > John Gabriel knows that elements being numbered is the same as being INDEXED or given a UNIQUE NAME. Learn from me, you syphilitic, stupid, jealous bastards!!!
> > > >
> > > >
> > > > Your moronic math professors and teachers DO NOT know or understand these things. They are my intellectual inferiors as are YOU!
> > > >
> > > >
> > > > All of you are not worth one turd of mine.
> > > What does it mean to index a set?
> > When you visit a library to find a particular book, do you not look it up in an index that tells you where that book is?
> >
> > Gosh, you are one prize moron.
> >
> > Here is a simpler example. Consider the set T={cars, airplanes, ships}. There are many types of cars and car dealers as there are airplanes and ships.
> >
> > We could create an index that goes something like this:
> >
> > 1 - Toyota (1)
> > BMW (2)
> > Mercedes (3)
> > etc
> > 2 - Mirage (1)
> > F16 (2)
> > Raptor (3)
> > etc
> > 3 - Cruiser (1)
> > Frigate (2)
> > Submarine (3)
> > etc
> > Now we have a lot of information about all these forms of transport but not enough memory. So what do we do, we store the information using an index. For example, we can say Description 2(3): Speed: Mach 2 and so on.
> >
> > In the same way, the father of all mainstream mathematical cranks such as yourself, realised that the set of Natural Numbers serves as a very good indexing tool.
> >
> > The reason the mythical set R is not countable is due to the fact that R does not exist! In other words, you cannot NAME the elements of R so that a natural number can be used to INDEX them. DO YOU UNDERSTAND NOW, YOU FUCKING MORON?
> > > what is the general definition of "indexing a set" then? How do we know if a set can be indexed or not?
> > BLAAAAAA DOOBI DDAAAAA Blurb dirb da da di di dum "I am a stupid Jew" - Markus Klyver.
> The examples you give are examples of indexing with natural numbers. But you said those are not the only indexes. Then, what do you mean by an "index"? The mainstream definition of countable defines countibility as indexing with natural numbers. You can't just change the definitions just because you feel like it and expect everyone to know you're inventing your own math and terminology.
>
> And stop hating Jews.

Shut up, moron!