Chris Angelico wrote: > On Thu, Sep 18, 2014 at 4:03 AM, Ian Kelly <ian.g.ke...@gmail.com> wrote: >> On Wed, Sep 17, 2014 at 9:10 AM, Chris Angelico <ros...@gmail.com> wrote: >>> And while it's >>> conceivable to define that infinity divided by anything is infinity, >>> and infinity modulo anything is zero, that raises serious issues of >>> primality and such; I'm not sure that that would really help anything. >> >> I missed that this point was already discussed. Can you elaborate on >> the "serious issues of primality and such"? Since infinity is not a >> natural number, its primality is undefined, so I don't see the issue >> here. > > It's not something I've personally worked with, so I'm trying to > dredge stuff up from my brain, but I think there's something along the > lines of "stuff shouldn't be a multiple of everything" and the Prime > Number Theorem. But that may just be a case where float != real.
I don't think that the Prime Number Theorem has anything to say about transfinite numbers (infinities). It says that for sufficiently large values of n, the number of primes below n asymptotically approaches the the integral of 1/ln(x) between 2 and n: π(n) ~ Li(n) (Note that in this case, π is not pi = 3.1414... but is the "prime counting function", thus proving that no matter how famous or well-known a particular mathematical symbol is, somebody will insist on using it for something else.) http://mathworld.wolfram.com/PrimeNumberTheorem.html Perhaps you are thinking of the Fundamental Theorem of Arithmetic, which states that every positive integer except 1 can be uniquely factorized into a product of one or more primes? http://mathworld.wolfram.com/FundamentalTheoremofArithmetic.html But that doesn't apply to infinity, which isn't an integer. -- Steven -- https://mail.python.org/mailman/listinfo/python-list
