the nicest proof of the infinitude of primes

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[EdBailey]

I really enjoy when Dr. Penn leverages technical methods to prove simple results. In this case, using ZF set theory and FToA and to recreate the Sieve of Eratosthenes

[RandomBurfness]

It should be noted that yes, while χ_(A union B) is indeed (ab)-periodic if χ_A has period a and χ_B has period b, the minimal period of the union is lcm(a, b).

[JM-usfr]

This looks similar to Furstenberg's topological proof of the infinitude of primes, but I like how it keeps it a little more accessible.

[archismanrudra]

Isn't this a reformulation of the topological proof of infinititude of primes?

[skylardeslypere]

The characteristic function of Z\A is also just 1 minus that of A.

[supratimsantra]

Congratulations a another's power of motivation . .

[omgopet]

Can you claim that everything has a prime factorization if there are finite primes? Doesn't proving that assume infinite primes?

[amirb]

in the last part which is the proof of the theorem, let's NOT assume we have finite # of primes. LEt's suppose we do have infinite # of primes. Then A is an infinite union of periodic sets (all A_p's are still periodic sets) and if it is periodic then we end up with the same contradiction (Z-A=(-1, 1) etc...) as in the video! So obviously something is not quite right here. I believe the union of periodic sets is only periodic if it is not an infinite union of sets (i.e. only if there are finite number of periodic sets) . This issue is not touched upon in the video

[balpedro]

The formula for the characteristic function of a union is an inmediate consequence of the inclusión/exclusión principle.

[Lucashallal]

Woah, this is a fascinatingly simple proof

[regimeoftruth]

Why did you add the product rather than subtract at 9:30?

[MasterHigure]

11:15 Isn't it just easier to write 1 - χ_A(n)?

[rafaelfreitas]

Nice video!
But shouldn't it be a negative sign at 09:49?

[cyrillechevallier]

That’s the best proof for infinite number of prime by FAR

[DaneBrooke]

Well, w/ respect, I disagree. Cuz I cannot explain this to a child, yet I *have* convinced children that there is an infinitude of primes.

[stephenhamer]

The ideas in play, here, are more interesting than the final proof, which is needlessly obscure. Euclid can rest easy tonight.
By the way, X(Z/A) = 1 - X(A), surely

[chessematics]

This is literally just Euclid's proof presented in this new language of periodic sets.