In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 13 Apr., 10:42, fom <fomJ...@nyms.net> wrote: > > On 4/13/2013 3:16 AM, WM wrote: > > > > > On 13 Apr., 06:47, "AMiews" <inva...@invalid.com> wrote: > > > > >>> every d_n of a numerical Cantor-list is the last digit of a > > >>> terminating decimal. > > >>> Never, do you understand, never anybody has seen or used a d_n that > > >>> does not belong to a terminating decimal. > > > > >> you seem confused by standard math notation here. Irrationals no one has > > >> seen the end. > > > > > But you believe in its existence nevertheless? > > > There is no end and there is no "all", because every scientific use of > > > "all" would include to find all. And that includes to prove that all > > > have been found. And that includes that a last one has been confirmed. > > > > WM's finite existence hypothesis. > > No, there is the simple fact that mathematics is done by finite means > and that statements concerning actions have to be proved,. It it not > sufficient to prove that if some axioms are given, that then things > have to be so and so.
That is how pure math is done. It avoids the ambiguity of wondering whether one's assumptions really are true.
It is only applied mathematicians and physicists and the like who have to worry about whether one's assumptions are all "true" enough in some sense to allow the resulting math to be applied somewhere outside of pure mathematics.
> But in doing > mathematics restrictions put by reality cannot be overcome.
Nonsense! A great deal of mathematics today, the pure kind, is done with little to no concern over whether one's assumptions conform to any sort of "reality". --