On 20 Apr., 17:15, fom <fomJ...@nyms.net> wrote: > On 4/20/2013 2:01 AM, WM wrote: > > > On 19 Apr., 21:41, Virgil <vir...@ligriv.com> wrote: > > >>> You have not understood the relativity of mathematics. There is no > >>> fixed largest number in mathematics. > > >> Because for every positive number, whether natural, integral, rational > >> or real, there is another twice as large > > > and finite and belonging to a finite set. > > >> As soon as any positive number has been identified, so has its double. > > > Not as soon! Every calculation, even the easiest, requires some time. > > But there is no calculation involved. Virgil's statement gives > no specific numerical value to which to apply the axioms.
No problem. Every numerical value is finite. The axioms are to be applied to finite naturals only, because only a finite natural changes its value when 1 is added. And the result is again a finite value, counting the elements of a finite set. This does never change.