On 5 Apr., 23:01, William Hughes <wpihug...@gmail.com> wrote:
> > > This depends on the finite subset removed. > > > If the finite set removed is E then > > > D\E has to remain. Note that whatever > > > subset E is chosen the number of lines > > > in D\E is infinite (but of course we > > > do not know which lines are in D\E). > > > How do you call a set E the number of elements exceeds any given > > natural number? > > E is a finite subset, thus the number of elements in E > equals some given finite number (we do not know which > finite number
Very interesting! You have my full support. Now there remains only a little step to do. Since you cannot find anything that is in D but not in E, we can extend your enlightenment: |N is a finite set. Thus the number of elements in |N equals some finite number. (You just conceded that such sets exist.) We do not know which finite number, but it is clear that the finite numbers count themselves and none counts aleph.