🧵 Untitled Thread
Anonymous at Mon, 6 May 2024 07:49:05 UTC No. 16161868
Let [math]a,b,c[/math] be the smallest side lengths such that [math]a^2+b^2 \neq c^2[/math]. Since [math]0^2+ 0^2 = 0^2[/math], these [math]a,b,c[/math] must be strictly positive. Now consider the triangle with side lengths [math]a/2,b/2,c/2[/math]. By minimality we have [math](a/2)^2+(b/2)^2 = (c/2)^2[/math]. Rearranging this yields: [math]a^2+b^2 = c^2[/math]. But now applying the transitivity of =, we arrive at [math]c^2 \neq c^2[/math], which is impossible.
Anonymous at Mon, 6 May 2024 09:42:13 UTC No. 16161955
What are you even trying to prove, the Pythagorean theorem?
>[math]a,b,c[/math] are rational or real numbers
Then you can't apply the well-ordering principle, because the rational/real numbers are not well-ordered.
>[math]a,b,c[/math] are integers
Then the smallest triangle not satisfying the Pythagorean identity is the equilateral triangle (1,1,1), and there are no smaller triangles with integer sides.
Anonymous at Mon, 6 May 2024 09:43:50 UTC No. 16161957
>>16161868
No such thing as smallest positive [math]a,b,c \in \mathbb{R} [/math] such that [math]a^2 + b^2 \neq c^2[/math].
Anonymous at Mon, 6 May 2024 12:07:12 UTC No. 16162167
>>16161957
1, 1, 1
Anonymous at Mon, 6 May 2024 12:28:58 UTC No. 16162193
>>16162167
1/2 is not an integer.
Anonymous at Mon, 6 May 2024 15:48:37 UTC No. 16162396
>>16161957
yeah thats what hes proving. dumbass
Anonymous at Mon, 6 May 2024 18:58:22 UTC No. 16162671
>>16162396
As if it isn't obvious by picking a = b = c arbitrarily small.
Anonymous at Mon, 6 May 2024 23:02:19 UTC No. 16163106
>>16162671
NTA but you can’t have a triangle with 3 sides the same length.
Anonymous at Tue, 7 May 2024 03:30:53 UTC No. 16163447
>>16163106
https://en.wikipedia.org/wiki/Equil
Anonymous at Tue, 7 May 2024 18:32:24 UTC No. 16164326
>>16161868
frog
Anonymous at Tue, 7 May 2024 18:40:49 UTC No. 16164344
>>16161868
>retard thinks there is "an infinitesimal", when there are infinitely many, and the opposite of "the infinity" is zero
read about non-standard analysis for once in your schizo life, retard
Anonymous at Tue, 7 May 2024 18:47:20 UTC No. 16164357
>>16163106
all my education has been a lie.
Anonymous at Tue, 7 May 2024 19:21:03 UTC No. 16164446
>>16161868
Consider, you found the smallest side lengths. Dividing smallest lengths in half does not create a smaller side length. See any 1 = 1 thread for further discussion.
Anonymous at Wed, 8 May 2024 08:39:56 UTC No. 16165503
>>16163106
Okay, but they can be infinitely close to the same size.
Anonymous at Wed, 8 May 2024 18:08:49 UTC No. 16166142
>>16163447
Literally impossible. Find me 3 pairs of rational numbers (q1,q2) which form an “equilateral” triangle. You cannot because if you could, the angle would be constructible by ruler and compass, and sqrt3 would be rational, both of which are retarded realbrained absurdities.
Anonymous at Wed, 8 May 2024 19:02:29 UTC No. 16166192
Thats becouse there are no smallest.
3/10000 4/10000 5/10000 is a valid pythagorean triple
Anonymous at Wed, 8 May 2024 19:13:20 UTC No. 16166204
>>16161868
Okay I'm only in undergrad, but maybe someone can explain to me that for any selected a2 + b2 ≠c2 (even if it wasn't a triangle)
How the fuck does dividing everything by 2 make ½(a2 + b2) suddenly equal to ½(c2) ?
Anonymous at Thu, 9 May 2024 06:49:04 UTC No. 16166932
>>16166204
The idea is that if didn't, it would contradict the minimality of a,b,c. OP is obviously retarded though