An excerpt from a new chapter in my book called The Ultimate Book of Numbers:

Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?

Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?

The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.

https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers

On Tuesday, August 29, 2023 at 4:13:30 AM UTC+3, Eram semper recta wrote:
> An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
>
> Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
>
> Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
>
> The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
>
> https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers

Of course, Sqrt2 is absolutely impossible to be measured by any decimal rationals, no matter what are the human advanced methods are used like those many as (Dedekind infamous cuts, Newton’s endless approximations, Intermediate no theorem, Godel's nonsense, Epsilon-delta eingineering, Caushy endless sequences, Euler's unfinished sums yet, ...., etc)

But miraculously, Sqrt2 exists as diagonal of square ⬛️ with unity side distance & was proven only from the greatest theorem as Phythagorus

Where only the unity distance can create it by one perpendicular to itself & thus Sqrt2 is a disaster hence an existing number that is not rational by any means

In fact Sqrt2 should be classified as rational simply because it can be ratiionalized in human minds so easily

But so unfortunately they were classified as irrational numbers simply because the were not a ratio of natural numbers

Inshort, the irrational "constructible "numbers are the creation of unity "one", where one cannot create any other types of alleged Real numbers like those believed & classified as "non-constructible " numbers like (Cubrt2 & Pi, e, log5, ..., etc)

Yes, even at the most foolish Paradise infinity ♾️, Sqrt2 can't be measured by any decimal rational number system for sure

BKK

tisdag 29 augusti 2023 kl. 03:13:30 UTC+2 skrev Eram semper recta:
> An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
>
> Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
>
> Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
>
> The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
>
> https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
The idea behind a cut is exactly that, we define a real number to be an ever so approaching approximation.

With your example, sqrt(2) "has itself as the least upper bound". Obviously we formalize this by defining real numbers in terms of rational ones.

On Tuesday, August 29, 2023 at 9:32:47 AM UTC+3, markus...@gmail.com wrote:
> tisdag 29 augusti 2023 kl. 03:13:30 UTC+2 skrev Eram semper recta:
> > An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
> >
> > Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
> >
> > Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
> >
> > The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
> >
> > https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
> The idea behind a cut is exactly that, we define a real number to be an ever so approaching approximation.
>
> With your example, sqrt(2) "has itself as the least upper bound". Obviously we formalize this by defining real numbers in terms of rational ones.

What you can't comprehend nor the mainstream academic proffessional mathematicians can't understand is the undeniable truth about every possible approximation is another distinct "constructible " number that is so irrelevant to the number in your mind, despite the human irrelevant feelings that they are close enough from the number in their minds

Simply because between any distinct constructible numbers, there are always & for ever many other constructible numbers & nothing else

Close enough, approximations, approaching fast or slow, nearly equal, & many alike terms are infact eingineering & scientific terms that don't mean anything in true untought mathematics

They Can't simply replace the equal "=" sign inorder to please the human mathematickers to achieve their endless huge fart & many false theories for sure

Bassam karzeddin 🔊

On Tuesday, August 29, 2023 at 9:32:47 AM UTC+3, markus...@gmail.com wrote:
> tisdag 29 augusti 2023 kl. 03:13:30 UTC+2 skrev Eram semper recta:
> > An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
> >
> > Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
> >
> > Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
> >
> > The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
> >
> > https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
> The idea behind a cut is exactly that, we define a real number to be an ever so approaching approximation.
>
> With your example, sqrt(2) "has itself as the least upper bound". Obviously we formalize this by defining real numbers in terms of rational ones.

To make you understand the truth of real numbers very fast, consider simply that latest obtained approximation of Sqrt2 as being approximated say for example for one thousand trillion decimal digits in 10-base number system, where that approximation is so simply a decimal RATIONAL number & never that irrational number in your mind (despite its absolute existence in its surd form only as was discovered few thousands years only & strictly from the Phythagorus theorem

However, your RATIONAL approximations would stay perpetually as RATIONAL (no matter if you fill the thousands of galaxies sizes with your digital approximation

And one more thing that a mid-school students must understand about their approximations, where there are always many more accurate RATIONAL approximations that humans cannot get by any imaginable technology where the case is SO perpetual

I.E, even the best RATIONAL or conservative approximations
Is impossible existence for sure 😕

BKk

Le 29/08/2023 à 15:50, bassam karzeddin a écrit :
> On Tuesday, August 29, 2023 at 9:32:47 AM UTC+3, markus...@gmail.com wrote:
>> tisdag 29 augusti 2023 kl. 03:13:30 UTC+2 skrev Eram semper recta:
>>> An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
>>>
>>> Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
>>>
>>> Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
>>>
>>> The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
>>>
>>> https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
>> The idea behind a cut is exactly that, we define a real number to be an ever so approaching approximation.
>>
>> With your example, sqrt(2) "has itself as the least upper bound". Obviously we formalize this by defining real numbers in terms of rational ones.
>
> To make you understand the truth of real numbers very fast, consider simply that latest obtained approximation of Sqrt2 as being approximated say for example for one thousand trillion decimal digits in 10-base number system, where that approximation is so simply a decimal RATIONAL number & never that irrational number in your mind (despite its absolute existence in its surd form only as was discovered few thousands years only & strictly from the Phythagorus theorem
>
> However, your RATIONAL approximations would stay perpetually as RATIONAL (no matter if you fill the thousands of galaxies sizes with your digital approximation
>
> And one more thing that a mid-school students must understand about their approximations, where there are always many more accurate RATIONAL approximations that humans cannot get by any imaginable technology where the case is SO perpetual
>
> I.E, even the best RATIONAL or conservative approximations
> Is impossible existence for sure 😕
>
> BKk = 💩 💩 💩

You're an idiot for sure, surer, surest and sureness Bassam.

Sad that your sibblings will find their name associated with so much
stupidity and rudeness for the centuries to come.

Does your family knows, Bassam?

On Monday, August 28, 2023 at 9:13:30 PM UTC-4, Eram semper recta wrote:
> An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
>
> Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
>
> Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
>
> The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
>
> https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers

I find similar discontent with the Dedekind cut. As if it resolved anything.. All that can be done to pin down the sqrt(2) is digit chasing.
It is a value and an operator; not a pure value. That mathematicians happily mix the two together as if they are one is not actually helpful.
The square root operator relies upon division, which is not a straightforward operation. The product is the straight-forward form. When does xx=2?

"At present, the root 2 value is computed to 10 trillion digits. For general use, its value is truncated and is used as 1.414 to make calculations easy. The fraction 99/70 is also sometimes used as the value of √2." - https://byjus.com/maths/square-root-of-2

As you've said, you can top it with all the prose you like, and as I recall I do like Dedekind's writing and thinking, but this 10 trillion digit value seems relevant still, doesn't it? Where we land is in the field of interpretation. As people puzzle over the reasonableness of an irrational value and make them 'official', then this matter of interpretation ensues. As physical correspondence goes the relevance of any of this is muted. As regards a value with an infinite quantity of digits, there are more computable values, such as 0.333...33, which can be incremented, and even squared. To work inductively all will be well, but the value has essentially a head and a tail, and that we can resolve here 0.333...34 could cause one to gawk at the ellipsis. Indeed, it's usage within mathematics implies a halting problem when this infinite form occurs, and lo and behold the usage of that decimal point in the old form 0.333... is problematic. The issuance of the digital value, followed by its ignorance in real analysis is somewhat the problem of the high-minded approach, as if saying: "let a be equal to the square root of two" resolved the whole thing immediately.

Prior to the irrational value, we'll have to let in rational values, and it's really back here that conflict arises more profoundly. To state that an integer divided by another integer can suddenly give birth to a continuum is a crock of pooey. Without a decimal point the whole thing is off. You'll be stuck with values and operators, and a set that does not compute why? Because the return value is one integer. That's known as closure. If your product has it then your division has it by definition. To admit that you'll have to throw away your remainder is a harsh reminder that division does not always compute. 3/5 is zero, by closure, sir. What magic happened that begot another answer? Certainly to claim that the discrete breeds the continuous is a lie, and we are still compromised by this lie. All that we can do is chase digits.

tisdag 29 augusti 2023 kl. 17:26:11 UTC+2 skrev Timothy Golden:
> On Monday, August 28, 2023 at 9:13:30 PM UTC-4, Eram semper recta wrote:
> > An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
> >
> > Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
> >
> > Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
> >
> > The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
> >
> > https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
> I find similar discontent with the Dedekind cut. As if it resolved anything. All that can be done to pin down the sqrt(2) is digit chasing.
> It is a value and an operator; not a pure value. That mathematicians happily mix the two together as if they are one is not actually helpful.
> The square root operator relies upon division, which is not a straightforward operation. The product is the straight-forward form. When does xx=2?
>
> "At present, the root 2 value is computed to 10 trillion digits. For general use, its value is truncated and is used as 1.414 to make calculations easy. The fraction 99/70 is also sometimes used as the value of √2." - https://byjus.com/maths/square-root-of-2
>
> As you've said, you can top it with all the prose you like, and as I recall I do like Dedekind's writing and thinking, but this 10 trillion digit value seems relevant still, doesn't it? Where we land is in the field of interpretation. As people puzzle over the reasonableness of an irrational value and make them 'official', then this matter of interpretation ensues. As physical correspondence goes the relevance of any of this is muted. As regards a value with an infinite quantity of digits, there are more computable values, such as 0.333...33, which can be incremented, and even squared. To work inductively all will be well, but the value has essentially a head and a tail, and that we can resolve here 0.333...34 could cause one to gawk at the ellipsis. Indeed, it's usage within mathematics implies a halting problem when this infinite form occurs, and lo and behold the usage of that decimal point in the old form 0.333... is problematic. The issuance of the digital value, followed by its ignorance in real analysis is somewhat the problem of the high-minded approach, as if saying: "let a be equal to the square root of two" resolved the whole thing immediately.
>
> Prior to the irrational value, we'll have to let in rational values, and it's really back here that conflict arises more profoundly. To state that an integer divided by another integer can suddenly give birth to a continuum is a crock of pooey. Without a decimal point the whole thing is off. You'll be stuck with values and operators, and a set that does not compute why? Because the return value is one integer. That's known as closure. If your product has it then your division has it by definition. To admit that you'll have to throw away your remainder is a harsh reminder that division does not always compute. 3/5 is zero, by closure, sir. What magic happened that begot another answer? Certainly to claim that the discrete breeds the continuous is a lie, and we are still compromised by this lie. All that we can do is chase digits.
The real number IS the cut. What's hard to understand about this?

On Tuesday, 29 August 2023 at 11:26:11 UTC-4, Timothy Golden wrote:
> On Monday, August 28, 2023 at 9:13:30 PM UTC-4, Eram semper recta wrote:
> > An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
> >
> > Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
> >
> > Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
> >
> > The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
> >
> > https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
> I find similar discontent with the Dedekind cut. As if it resolved anything. All that can be done to pin down the sqrt(2) is digit chasing.

Not even 'digit chasing' because no matter how many digits, you never have square root of two. All you have is the symbol √2
which stands for an approximated constant.

> It is a value and an operator; not a pure value.

Right. 2 under the radical.

> That mathematicians happily mix the two together as if they are one is not actually helpful.
> The square root operator relies upon division, which is not a straightforward operation.

Nope. That is untrue.

> The product is the straight-forward form. When does xx=2?
>
> "At present, the root 2 value is computed to 10 trillion digits. For general use, its value is truncated and is used as 1.414 to make calculations easy. The fraction 99/70 is also sometimes used as the value of √2." - https://byjus.com/maths/square-root-of-2
>
> As you've said, you can top it with all the prose you like, and as I recall I do like Dedekind's writing and thinking, but this 10 trillion digit value seems relevant still, doesn't it? Where we land is in the field of interpretation. As people puzzle over the reasonableness of an irrational value and make them 'official', then this matter of interpretation ensues. As physical correspondence goes the relevance of any of this is muted. As regards a value with an infinite quantity of digits, there are more computable values, such as 0.333...33, which can be incremented, and even squared. To work inductively all will be well, but the value has essentially a head and a tail, and that we can resolve here 0.333...34 could cause one to gawk at the ellipsis. Indeed, it's usage within mathematics implies a halting problem when this infinite form occurs, and lo and behold the usage of that decimal point in the old form 0.333... is problematic. The issuance of the digital value, followed by its ignorance in real analysis is somewhat the problem of the high-minded approach, as if saying: "let a be equal to the square root of two" resolved the whole thing immediately.
>
> Prior to the irrational value, we'll have to let in rational values, and it's really back here that conflict arises more profoundly. To state that an integer divided by another integer can suddenly give birth to a continuum is a crock of pooey. Without a decimal point the whole thing is off. You'll be stuck with values and operators, and a set that does not compute why? Because the return value is one integer. That's known as closure. If your product has it then your division has it by definition. To admit that you'll have to throw away your remainder is a harsh reminder that division does not always compute. 3/5 is zero, by closure, sir. What magic happened that begot another answer? Certainly to claim that the discrete breeds the continuous is a lie, and we are still compromised by this lie. All that we can do is chase digits.

On Tuesday, 29 August 2023 at 09:57:00 UTC-4, Python wrote:
> Le 29/08/2023 à 15:50,
> >>> An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
> >>>
> >>> Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
> >>>
> >>> Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
> >>>
> >>> The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap.. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
> >>>
> >>> https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
> >> The idea behind a cut is exactly that, we define a real number to be an ever so approaching approximation.
> >>
> >> With your example, sqrt(2) "has itself as the least upper bound". Obviously we formalize this by defining real numbers in terms of rational ones.
> >
> > To make you understand the truth of real numbers very fast, consider simply that latest obtained approximation of Sqrt2 as being approximated say for example for one thousand trillion decimal digits in 10-base number system, where that approximation is so simply a decimal RATIONAL number & never that irrational number in your mind (despite its absolute existence in its surd form only as was discovered few thousands years only & strictly from the Phythagorus theorem
> >
> > However, your RATIONAL approximations would stay perpetually as RATIONAL (no matter if you fill the thousands of galaxies sizes with your digital approximation
> >
> > And one more thing that a mid-school students must understand about their approximations, where there are always many more accurate RATIONAL approximations that humans cannot get by any imaginable technology where the case is SO perpetual
> >
> > I.E, even the best RATIONAL or conservative approximations
> > Is impossible existence for sure 😕
> >
> > BKk = 💩 💩 💩
>
> You're an idiot for sure, surer, surest and sureness Bassam.
>
> Sad that your sibblings will find their name associated with so much
> stupidity and rudeness for the centuries to come.

Look who is talking!
It's like Trump calling Christie a fat pig.

>
> Does your family knows, Bassam?

Your students know by now what a moron you are Jean Pierre Messager (aka YBM, JPM, Python, Shithead, etc).

On Tuesday, August 29, 2023 at 4:32:00 PM UTC+3, bassam karzeddin wrote:
> On Tuesday, August 29, 2023 at 9:32:47 AM UTC+3, markus...@gmail.com wrote:
> > tisdag 29 augusti 2023 kl. 03:13:30 UTC+2 skrev Eram semper recta:
> > > An excerpt from a new chapter in my book called The Ultimate Book of Numbers:
> > >
> > > Dedekind claimed foolishly that 2={D,U}. But in what way does Dedekind describe the incommensurable magnitude sqrt(2)?
> > >
> > > Does he describe it exactly in terms of rational numbers? Can sqrt(2) be measured using the definition 2={D,U}?
> > >
> > > The answer is clearly no. Dedekind's approach does not provide an exact measure of sqrt(2) in rational terms. At best, it approximates the incommensurable ratio by sandwiching it between rational bounds. But an approximation or partial measure does not constitute a proper number. A true number requires an exact measure of a ratio between magnitudes, not a vague cut between sets of rationals. Dedekind's failure lies in conflating partial bounds with precise measures. His irrational cuts do not define numbers, but rather gesture vaguely at incommensurable ratios beyond numeric reach. No amount of hand-waving about completeness can bridge this basic conceptual gap.. Without exact measure, there are no real numbers - only rational approximations of that which lies beyond finite comparison. Dedekind’s mystical “real” number line has no clothes, no matter the quality of prose used to describe the imaginary attire.
> > >
> > > https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
> > The idea behind a cut is exactly that, we define a real number to be an ever so approaching approximation.
> >
> > With your example, sqrt(2) "has itself as the least upper bound". Obviously we formalize this by defining real numbers in terms of rational ones.
> What you can't comprehend nor the mainstream academic proffessional mathematicians can't understand is the undeniable truth about every possible approximation is another distinct "constructible " number that is so irrelevant to the number in your mind, despite the human irrelevant feelings that they are close enough from the number in their minds
>
> Simply because between any distinct constructible numbers, there are always & for ever many other constructible numbers & nothing else
>
> Close enough, approximations, approaching fast or slow, nearly equal, & many alike terms are infact eingineering & scientific terms that don't mean anything in true untought mathematics
>
> They Can't simply replace the equal "=" sign inorder to please the human mathematickers to achieve their endless huge fart & many false theories for sure
>
> Bassam karzeddin 🔊