Pigeonhole via functions.

We look at a formulation of the pigeonhole principle using functions.

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Books I like:

Abstract Algebra:

Differential Forms:

Number Theory:

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[tavishbryan]

Wow the real world example really helped this sink in. Thank you for your great content and hard work!

[jesusalej]

It is not the same. We will not see your great and awesome smile anymore! Anyway it is not a good place to stop... watching your videos.

[JasonOvalles]

What software did you use for the slides/writing on screen? I've been trying to find something that works well for my online classes, but have had little luck so far.

[prbprb]

Michael, since you are so good at number theory, can you please do a video on when expressions like sqrt(n + m sqrt(3)) can be solved by a +b sqrt(3), and the theory behind it? I know there ia a deep theory

[noahtaul]

Better to put pigeons into holes than to put holes into pigeons!

[tomatrix]

Love these supplementary uploads. Good idea

[theproofessayist]

Dear Michael or anyone else in the comments. What proposition corresponding to mapping terms would we get if the cardinality of your domain and codomain set WERE EQUAL?

[lori]

Is it knocking o are the renovations making themselves heard?

[marcusdecarvalho]

Sorry, but: "If you try and place 'm' pigeons in 'n' holes, where 'm' < 'n', then there will be at least one hole which is unfilled."

[trueriver]

1:01 This is just An excuse to talk about pigeons while writing poo on the board, those birds being famous for producing that substance...

and introducing said white fluid onto the hair of unwitting humans. Is this what inspired the real world example?

[kouverbingham]

please make a video about how we dont know whether pi+e is rational or not, and how pathetic that is

[bibeksubedii]

You have found the secret way to make your channel blow up
Just remember me when you get famous, will you ?

[JB-ymup]

There are not 100 million elements in B