In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
Set theoretic cardinality is defined by existence or non-existence of surjections from one set to another. And outside of WMYTHEOLOGY all sets, even non-finite ones, are actual. > > > > > > 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.
Since your C4 is clearly not one of C1,C2 or C3, why should it make any of them relevant to anything except the idiocy of WMYTHEOLOGY ? --