I Proved the Pigeonhole Principle (Or Did I?)

📊 Do you need PRIVATE CLASSES on Math & Physics, or do you know somebody who does? I might be helpful! My personal Whatsapp and email: [phone] ; [e-mail]
😎 Become a member to have exclusive access:
/ @dibeos
📈 Check out my Udemy courses (you may find something that interests you 😉): www.udemy.com/...
🔔 Subscribe:
/ @dibeos
🥹 Consider supporting us on Patreon:
www.patreon.co...

[@jaychristianleria5476]

That's my Math Professor who could be brown, who could be blue, who could be violet sky
he could be hurtful, he could be purple, he could be anything I like

[@dibeos]

You’re absolutely right 👍

[@MrBeklager]

I heard «Silly function» when you said «ceiling function»😂

[@dibeos]

@@MrBeklager me too Hahahha actually I noticed only after posting that it sounds like silly function hahahah I need to work on my accent 😅😎

[@samueldeandrade8535]

This was a thousand times better than proofs of other channels. Straight to the point, intuitive, basic, as it should be.

[@dibeos]

@@samueldeandrade8535 thanks!!! 🙏🏻 what other proofs out there are usually confusing in your opinion?

[@Arthur-vo9kt]

What is your nationality? I mean, are you brazilian? Your accent sounds so nice to hear

[@dibeos]

@@Arthur-vo9kt hi Arthur, yes I’m Brazilian 😎

[@aggking7034]

1:46 I didn't understand why (k+1)n-k=n

[@dibeos]

That’s because it’s a typo. I just wrote it wrong. My bad. If you see our initial assumption in the general form of the principle, we had kn items. So I meant (k+1)n-nk=n. Thanks for noticing and pointing it out.

[@aggking7034]

@@dibeos Got it, thanks👍🏻

[@thedude882]

Nice! Your first proof can also be adapted to prove the infinite pidgeonhole principle.
The pidgeonhole principle is applied to Ramsey Theory and can also be used to solve this little problem I love:
Given 5 points on a sphere, there's an emisphere that contains at least 4 of them.

[@dibeos]

@@thedude882 oh yeah, this one of the sphere I’ve already seen. But how is this one of the infinite pigeonhole?

[@thedude882]

@@dibeos If you place infinitely many pidgeons into finitely many holes, at least one hole will contain infinitely many pidgeons.

[@willnewman9783]

You didn't prove it, yet again. Your proof of the generalized version is fatally flawed.
You say by induction one container has k items. Then you use normal pigeon hole to find a specific container, and then you put the k items into this one. But this does not need to be where the k items originally were. You are not allowed to move items between containers.

[@dibeos]

@@willnewman9783 why not? 🤔

[@willnewman9783]

@@dibeos The statement says that if you put n balls into m urns, you can find an urn with at least ceiling(n/m) balls, not that you can arrange things so that this is true.
If you were allowed to rearange, you might as well put all n balls into a single urn.

[@SobTim-eu3xu]

Yay, new video)