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. But mathematical things are charaterized and defined by properties they have, not by properties they are missing. In particular numbers like Cantor's diagonal are defined by the digits they have and not by missing digits.
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).