🧵 Proof of the irrationality of square root of 2
Anonymous at Fri, 12 Jul 2024 09:02:35 UTC No. 16278480
I recently came across this website that compiles proofs of the irrationality of square root of two or some generalizations of that results, what's your favorite one? Mine has to be the first one by Richard Dedekind, seems so elegant and doesn't rely on too much number theory.
Here's the compilation: https://www.cut-the-knot.org/proofs
Anonymous at Fri, 12 Jul 2024 13:10:57 UTC No. 16278695
>>16278480
>what's your favorite one?
8''', because it can be adapted into a kinesthetic proof (pic related) that can be understood using only whole-number addition, subtraction, and multiplication.
Anonymous at Fri, 12 Jul 2024 13:22:39 UTC No. 16278703
√2 is irrational so we can't really draw a line of length √2. How is it possible to have the hypotenuse of √2 in that picture?
Anonymous at Fri, 12 Jul 2024 13:24:41 UTC No. 16278705
>>16278480
what happens if you make the vertical leg [math]i[/math]
Anonymous at Fri, 12 Jul 2024 18:07:31 UTC No. 16279054
>>16278703
How's that different from any other line. You can't really draw a line with exact length of 1.00000...
Anonymous at Fri, 12 Jul 2024 18:40:14 UTC No. 16279106
>>16279054
Exactly, so the proof in pic is wrong. Mathematics may cope saying it's a hypothetical scenario lmao
Anonymous at Fri, 12 Jul 2024 18:49:54 UTC No. 16279121
>>16279106
Are you retarded? The accuracy of the picture has nothing to do with the proofs.
Anonymous at Fri, 12 Jul 2024 19:33:16 UTC No. 16279199
>>16279121
Why tf did op use it then
Anonymous at Fri, 12 Jul 2024 22:58:22 UTC No. 16279504
>>16278480
Proof 8" because I'm 8" bone pressed
Anonymous at Fri, 12 Jul 2024 23:44:22 UTC No. 16279559
>>16279054
Yes I can, just define the side as 1 unit of whatever measurements you want, let's use the anon for length. Make a 1 by 1 square and say it has 1 anon length sides. The diagonal is √2 anon