Friday, January 8, 2016

are there infinitely more primes numbers than composites numbers?

this is a cool question, presented in my 11am honors class by A & B (physics & computer science majors).

are you an idealist or intuitionist in mathematics?*

the idealist relies on aprioristic deduction results, the realist goes empirical. she counts ("she" is a computer algorithm). so, i took a realist short cut and then made my best inference. something very interesting happens to primes -between 106 and 108, which allows for siding in favor of composite numbers' greater "infinite-density."

my hunch is that Q> P.

* the intuitionist claims that p is true means that there is a proof of p.  from the idealist (platonist) perspective, whether or not we have a proof, we know that p must be either true or false: mathematical reality guarantees that it has one of these two truth-values. the intuitionist dithers.

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