In article <email@example.com>, firstname.lastname@example.org wrote:
> On Tuesday, 16 July 2013 10:06:37 UTC+2, Virgil wrote:
> >> What turns a potentially set of "every FIS" into the actually infinite > >> set of "all n or all FIS". > > > Among other things, that there is no finite limit to the number of FISONs, > > or of naturals. > > Other things include blue blossoms, deep water, and yellow stars.
Perhaps WM's blue blossoms, deep water, and yellow stars are alowed ro prove things in WM's wild weird world of WMytheology , but they don't in honest mathematics.
> mathematical things are charaterized and defined by properties they have
Mathematical things are defined by definitions, at least everywhere outside of WM's wild weird world of WMytheology.
> In particular numbers like Cantor's diagonal > are defined by the digits they have and not by missing digits.
Given any list of reals in which the nth number is known accurately to n decimal places, nonmembers of that list can be defined. > > But it is clear, in order to distinguish 0.111... from all its finite > approximations there is nothing available but a multiset of belief (and a > finite definition - but there are only countably many finite definitions).
Thus WM claims that a non-terminating decimal, such as the one for 1/9, cannot be distinguished from any of its truncated thus terminating decimal approximations.
However, everywhere outside of WM's wild weird world of WMytheology, it is a trivial task, easily accomplished by anyone other than WM himslf. --