On 29 Jan., 14:27, William Hughes <wpihug...@gmail.com> wrote: > On Jan 29, 12:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 29 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote: > > > > To summarize > > > > For every natural number, n, the antidiagonal,d, of a list L > > > is not equal to the nth line of L > > > > A statement WM has made. > > > > A) For every natural number n, P(n) is true. > > > implies > > > B) There does not exist a natural number n such that P(n) is > > > false. > > > > A statement WM has made. > > > > There does not exist a natural number n such that d is > > > equal to the nth line of L > > > > A statement WM disputes > > > I do not dispute this statement (as I erroneously had said yesterday, > > when being in a hurry). I dispute that this statement implies the > > statement: > > d is not in one of all lines of the infinite list L > > It does, however, imply that d is not > of the the lines of the infinite list L.
Here we have again the ambivalence required for set theory. No, your statement is incorrect if "infinite" is used in the sense of completed or actual, i.e., in the only sense that would allow for set theoretic cardinality.
> > > and, hence, cannot > > be used to argue that cardinality is increased. > > (The reson is that "all" is maeningless here.) > > > What about C1, C2, C3? > > I neither know nor care.-
You should. In the case of all terminating decimals, for instance, C4 is obviously wrong.