Re:A One-Line Proof of the Infinitude of Primes
by JadeNB on Tuesday November 15, 2016 @03:18PM
(#12961791)
> And actually any periodic function that is zero somewhere could be used in a tiny bit modified version of this proof.
I think that, for the modification to be tiny, you need something like: there is an interval on which the function is positive, and on the boundary of which it vanishes. (Some sign condition is necessary; taking the constant function at 0 doesn't work! Of course, this particular condition is automatically satisfied for any continuous, periodic function that vanishes somewhere, but is not identically 0.)
I think that, for the modification to be tiny, you need something like: there is an interval on which the function is positive, and on the boundary of which it vanishes. (Some sign condition is necessary; taking the constant function at 0 doesn't work! Of course, this particular condition is automatically satisfied for any continuous, periodic function that vanishes somewhere, but is not identically 0.)