In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 23 Feb., 16:54, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 23, 1:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > >
> > Are the statements > > > > There exists a natural number > > m such that the mth line of L > > has property P. > > > > There does not exist a natural number > > m such that the mth line of L > > has property P. > > > > contradictory? > > Not if you mean by "to exist" in the first case " we can find" and in > the second case "we can prove".
In mathematics, as distinguished for WMytheology, proofs of existence do not always require that one find an example of the thing claimed to exist. >
> > ====================== > > Can you identify a FIS of d that is not in a line l of L? > > > > No
Can you identify a line l of L that is not exceeded by any preassigned finite number of FISs?
> > Why then are you raising the impression as if you were trying to argue > that d is not with *all its existence* in the lines of the list?
What we are arguing is that d is not equal to any line of the list and is has many FISs longer than any given line of the list, and is thus not a member of the list.a
The argument is similar to, and at least as valid as, the Cantor argument that no list of binary sequences can exhaust the set of all infinite binary sequences.
And WM has yet to come up with a counterargument to Cantor's diagonal argument that holds outside WMytheology. --