This Will Be Your Favorite Simple Problem

Here's a result that, at first, is quite hard to believe. However, a little bit of logic can go a long way.
This is one of my favorite simple math problems in the world. Enjoy!

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

#math #brithemathguy #irrationalnumber

[BriTheMathGuy]

🎓Become a Math Master With My Intro To Proofs Course!

[sodiboo]

i love when you pick sqrt(2) every single time for every number, it reminds me of that one video where it's like "that's right, it goes in the square hole!" for *every single shape*

[timurpryadilin]

i mean e^ln2=2, wgich is much more straightforward, assuming we know irrationality of e and ln2

[BriTheMathGuy]

I have now realized I hate the way I say "irrational"

[Mehraj_IITKGP]

Reminded me of my elementary school days when I asked my math teacher the same question. Well, he resolved it by saying e^{ln(2)}=2.
Your explanation is also awesome:)

[AquaticDot]

My immediate first thought was e^ln3, for example. I feel like exponentials and logs would be the most natural first choice.

[bendriver]

This has always been my favourite proof, using an undecided (undecidable?) fact to prove another conjecture. I understand that Wiles’ proof of Fernat’s Last Theirem depends on a similar logical partition (ie considering X and not X separately and showing that something is true either way). So elegant! Thank you for making this video.

[eduardoeller]

This IS my favorite simple theorem, thank you so much for covering it!!!! :)

[MatesMike]

It feels weird to consider r as a rational xD But anyway, nice video as always :)

[japanada]

For a nice constructive example with an easy proof: (sqrt(2)) ^ x = 3, where x is the log base sqrt(2) of 3. If x were rational, say x=p/q, then sqrt(2)^p = 3^q, and squaring both sides, 2^p = 9^q; contradiction because one side is even and the other is odd.

(Many people have pointed out e^(ln2)=2, but it is quite difficult to prove ln2 is irrational. Numbers of the form log_a(b), where a and b are rational powers of rational numbers, are some of the easiest numbers to prove irrationality for - even easier than sqrt(2) in my opinion - because it just boils down to comparing the prime factorizations of a and b)

[hessek]

This is literally one of the first proofs we are tought about in my introduction to proofs calss. Nice

[matt-tutorials]

I love your content. It makes so much sense. The way you explain things is so much better than how most of these school teachers try and explain stuff! There's some great ideas which I may use for my youtube channel! Thanks!

[alienbroccoli]

Its just like what Matt Parker said on his channel
π^π^π^π could be an integer as far as we know

[pinedelgado]

I'm a math nut and this is my newest favorite math video!! Thank you lots for posting!!

[agape_]

You know that a video is good when you feel like it did last ~10% of its actual duration

[ShefsofProblemSolving]

This is one of my favorite introductory problems in Number Theory and how to think about proving stuff! If A then done, else not A implies B so done

[michaelzumpano]

I really loved the reveal. You’re right, it’s simply my irrational favorite! I’m going to watch it again.

[pranaymondal]

Math is so amazing, it confuses us not giving a single clue, and the next moment it becomes totally known to us

[jakubledl]

My favourite example of the importance of constructive math.

[DeemIsTaken]

"Teacher, when are we gonna need this in real life?" "Imagine youre at the grocery store..."