On Feb 7, 10:18 am, WM <mueck...@rz.fh-augsburg.de> wrote: > On 7 Feb., 10:11, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Feb 7, 10:05 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 7 Feb., 10:03, William Hughes <wpihug...@gmail.com> wrote: > > > > > On Feb 7, 7:45 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > Matheology § 222 Back to the roots > > > > > > Consider a Cantor-list with entries a_n and anti-diagonal d: > > > > > Then, according to WM, d is not a line of the list. > > > > Do you agree that the logic applied in set theory does not make a > > > difference between "for every" and "for all"? > > > Can you explain why here, in this decisive case, a difference appears > > > nevertheless? > > > Since neither standard set theory, nor the concept "all" is used > > by WM in obtaining "d is not a line of the list" > > I don't know what you mean by "a difference appears". > > Look at the original post. Standard set theory is applied.
WM uses induction to show that for every natural number n, d is not the nth line of the list. He then uses the fact that this is equivalent to "there does not exist an m, such that d is the mth line of the list". At no time does he assume that "all" lines exist.
