On Sunday, November 8, 2020 at 1:46:41 PM UTC+2, Bassam Karzeddin wrote:
> The few hired Incurable resident Morons on sci. math since many years like (Python. Dan C-T, Zelo M, ..., etc) want to convince the very clueless persons that irrational number is a recent discovery coming from more insane and mindless cheaters like (Cantor, Cashy, Dedikined, Galois, Cardano, ..., etc)
>
> As if it was never discovered a few thousands of years back from the original "Summaries" theorem (later was named illegally by biased historians as the Pythagorean theorem-who did never prove it despite having hundreds of simple elementary proofs nowadays)
>
> This is usually how true discoveries are generally attributed to non-deservedly people strictly in the history of mathematics and science as well
>
> However, None of the above mentioned many historical names was able to discover any real (existing) number by their endless fart methods and very useless acts
>
> Where the true (existing) irrational numbers were long ago discovered and being noted as constructible numbers since they are already existing
>
> And the "Sumerians" theorem doesn't work at all with non-constructible numbers
>
> Adding another too simple challenge to all humans (not necessarily only for the academic, professional mathematicians) is this challenge:
>
> "Can you find *EXACTLY* a single significant triangle with at least one side (as non-constructible numbr)?
>
> Then let the whole world see your alleged existing and exciting triangle under your true identity name in order that future creatures may remember one day your case for a truer future historical record
>
> Have fun ...
>
> Bassam KARZEDDIN
> On Friday, November 6, 2020 at 7:48:45 PM UTC+3, Python wrote:
> > David Petry wrote:
> > > On Sunday, November 1, 2020 at 6:46:10 PM UTC-8, David Petry wrote:
> > >> It must have been twenty or so years ago that someone in this newsgroup (I forget who) said that the diagonal argument can prove the existence of irrational numbers, and two mathematicians (I'm pretty sure it was David Ullrich and Lee Rudolf) mocked the idea. They seemed to think it was absurd. So I showed them how it can be done.
> > >>
> > >> Simply start with a precisely defined enumeration of rational numbers between zero and one, and then apply the diagonal argument to the list of decimal expansions of those rational numbers. The technical detail of what to do with rational numbers that have two expansions is easily dealt with, and in the end, we get a well defined irrational number with an algorithm to compute its digits. An we don't need to invoke the idea of uncountable infinities to do the proof.
> > >>
> > >> So it seems that mathematicians in general do not realize that the diagonal argument can easily be used to prove the existence of irrational numbers and that the introduction of uncountable infinities is not an essential part of the argument.
> > >>
> > >> So here's something I'd like people to think about.
> > >>
> > >> When I learned about Cantor's proof (I was 13 years old, in 8'th grade), we were not shown how the diagonal argument can be used to prove the existence of irrational numbers. But what if we had been shown that proof?
> > >>
> > >> Then it's likely that students would have demanded to know why couldn't the diagonal argument also be used too produce an algorithm for computing the digits of a transcendental number, and why we had been introduced to the notion of uncountable sets. Because it seems clear that the notion of uncountable infinites is dubious at best, and has no connection to all of the other mathematics we were learning, all of which was used to solve real world problems, and that the notion of uncountable sets is not even needed for the "application" for which it was used!
> > >> So the point is that it is entirely reasonable for young students to believe that they were deceived and lied to. That is, they were deliberately not shown something that would quickly have lead to questions that the teachers would not be able to answer.
> > >>
> > >> So it's not the least bit surprising that so many people in this newsgroup insist that something is very wrong with Cantor's Diagonal argument which makes use of the notion of uncountable infinities. However, I must admit, most of those people don't see clearly what's going on. But neither do the "mathematicians" who mock them.
> > >
> > >
> > >
> > > Someone doubted that Ullrich and Rudolph really didn't know that the diagonal argument could be used to prove the existence of irrational numbers, so I looked it up. Here's how it went:
> > >
> > > David Ullrich wrote:
> > >> (Or maybe I'm wrong - how _does_ one give a proof that there
> > >> exist irrational numbers by "diagonalization"?
> > >
> > > Lee Rudolph responded:
> > > Well, duh. sqrt(2) is the *diagonal* of the unit square, right?
> >
> > Well, it's quite a pun on you, a nice one, I have to admit. You
> > missed it unfortunately.
> >
> > In no way it's a rebuttal on a diagonal argument (in Cantor's way)
> > applied to a list of rational numbers to be a proof that irrational
> > numbers exist. As a matter of fact it is, as said quite overkill.
> >
> > Come on, David, don't you have the basic ability in math and logic
> > in order to figure that our for yourself? I asked myself the very
> > same question in first year of University when presented with
> > Cantor's diagonal argument, I figured out myself, and had then a
> > nice drink with friends. What were you doing then?

Go verify my claims too lazy historians

Bkk 🔊