In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 21 Feb., 14:18, William Hughes <wpihug...@gmail.com> wrote: > > According to WM > > > > i.; > > > > A) For every natural number n, P(n) is true. > > implies > > that this claim A holds for every natural number from 1 to n, but not > necessarily for infinitely many following.
Then WM has dumped proofs by induction right out the window. > > > B) There does not exist a natural number n such that P(n) is > > false. > > In potential infinity
There can be no such thing as potential infinity until WM or someone else can produce an axiom system for it that at least does not contain any of the obvious flaws that WM's version of it has.
> you have to distinguish between existence and > the possibility to identify.
We do nt have to do any such thing. If WM choses to, since it only holds in his WMytheology and not elsewhere, no one need conform to WM's private insanity.
> Every potentially infinite set of natural numbers has a last element. > But you cannot identify it.
Then it is no more actual than inaccessible real numbers.
> > You have to find a d_n that is not in any line.
Nope, all you have to find is a d which is not in any line, and since d does not have a maximal FIS length, that is trivial.
> Of course d is in the list as a line unless you can show a missing > d_n.
Not outside WMytheology.
Outside WMytheology. to show that d is a line, you must be able to find that line in your list of lines.
Inside WMytheology, apparently anything that one fails to disprove must b true. --