In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 25 Jan., 01:27, William Hughes <wpihug...@gmail.com> wrote: > > > Outside of Wolkenmukenheim it is clear that an infinite set can be the > > union > > of finite sets.- > > But in mathematics it is clear that a strictly increasing sequence > does not contain its limit.
That hardly proves that that limit does not exist, as WM claims.
> Each one of infinitely many terms fails to > reach the limit.
Each of the infinitely many terms of f(n) = (n-1)/n fails to reach the limit, but that limit exists.
> And this case is given by the sequence of finite > initial segments of natural numbers.
Each of those infinitely many finite initial segments of naturals fails to reach the limit, but that limit exists in ZF, and in any sane set theory that I am familiar with. --