I bet you haven't seen this proof for irrationality of square root of two

Dive into the captivating world of mathematics with our latest video, "Unraveling the Mystery: The Quest for the Irrational Square Root of 2." Join us on a journey where we explore the intricacies of rational numbers, confront the challenges posed by floating-point arithmetic, and embark on a quest to find natural numbers a and b such that (a/b)^2 equals two. Discover the twists and turns as we decode patterns, grapple with fitness functions, and ultimately conclude whether the square root of 2 is truly irrational. Let the adventure begin, and don't forget to share your thoughts in the comments section below! Happy pondering!
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[@academyofuselessideas]

There are many proofs of the irrationality of square root of two. Gorlack invites you to write your own, or to write down the one presented here! You can find a written version of the proof presented here (I haven't seen this proof presented in many places). If you want to share your proofs, or to get a written version of this proof feel free to join our discord server! (If you would like the proof to be written here as well, leave a comment!... (It would be cool if youtube comments rendered LaTeX, wouldn't that be awesome?))

[@ChaoticMagnet]

LaTeX on KZbin would be awesome

[@academyofuselessideas]

@@ChaoticMagnet I wonder if could make that suggestion somewhere 🤔

[@jeevacation]

This is interesting though most of it flew over my head. What I learned was the basic odd and even contradiction. I didn't know other proofs could exist. I quickly realized after doing the odd and even contradiction that it was only relevant for sqrt(2) and wouldn't work for testing other numbers. The textbook I used also said that pi took very long to prove that it was irrational. Very interesting video. Thank you for posting.

[@academyofuselessideas]

You're referring to the classic proof... Someone just showed me a viral video of Taylor Swift explaining that proof... The even and odd proof is easy to generalize to the square root of any prime number (i bet you can do that generalization)... There are many proofs indeed... each proof gives you different insights... I don't think the proof I presented is that easy to find which is in part why I chose it... in any case, I hope you found the video helpful!

[@jeevacation]

I'll try to think of the generalization later but yes the video gave me new insights so yes, very helpful. Thank you for publishing@@academyofuselessideas