🚀 go-pugleaf

>
>But if I hypothesize that in nature, there a way to  to order nothing
>(0!=1), versus the null hypothesis that there is no way to order nothing
>(0!=0), how will we set about testing the hypothesis?
>
>Regards,
>Jim Sarbeck

0! = 1 is the definition of 0!, not some rationalizing whether there is one or
no ways to order nothing.  The choice to define 0! as 1 is because the Gamma
function, which models the discrete factorial function to the continuous has
the value Gamma(1)=1 where Gamma(1) = 0!.  So, by specialization of the Gamma
function to the non-negative integers, we get 0! = 1.  But, if you want to
argue it by rationalizing, you could say 0! is anything.

As for math being a process of discovery or invention, it is both.  There are
people who create new items.  12 dimensional manifolds with constant
ricci curvatures, etc. are figments of human thought, created out of thin air
based on rules that are also created.  However, one can also think that these
manifolds are discovered.

Until you can pin down an exact definition of invention and discovery, I'd
say the blurriness is due to an inexact definition of these words.

EDEW