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We know it can be written out as a haiku: https://xkcd.com/622/ https://xkcd.com/622/!
by quantumtremor 10y ago
We know it can be written out as a haiku: https://xkcd.com/622/ https://xkcd.com/622/!
- schoen 10y agoWhile that's very clever, it doesn't accurately present Euclid's argument because the haiku is Top prime's divisors' product (plus one)'s factors are...? Q.E.D., bitches! This doesn't include Euclid's argument about multiplying all of the primes, mistakenly referring instead to "top prime's divisors". The "top prime's divisors' product" would be equal to the top prime itself, so Randall's haiku asks "if there is a largest prime p, what are the divisors of (p+1)?" which doesn't create any contradiction (it could simply be divisible by various smaller primes!). Maybe we should amend it to Take factorial of top prime, then add one: what are the divisors?
- adrianratnapala 10y agoIt's not the factorial either, that would include composites in the product too.
- schoen 10y agoEuclid didn't use the factorial in his original proof, but it still produces a logically correct argument and it has fewer syllables. Metri causa. :-)
- JadeNB 10y agoUsing the factorial is better, I think, even if ahistorical; it avoids the slight unpleasantness of having to show that every non-unit integer is divisible by a prime.
- wangarific 10y agoBut then you can't exclaim Q.E.D., bitches! and it would be a terrible cartoon. :)
- schoen 10y agoIt's restored in a version further down in the thread.
- JadeNB 10y agoCouldn't you just change "divisors' product" to "factorial's"? I guess that it does some violence to the metre.
- schoen 10y agoYou could work with it and get the original last line back: Factorial of top prime, plus one: factor that! Q.E.D., bitches!