On 21 Feb., 20:23, William Hughes <wpihug...@gmail.com> wrote: > On Feb 21, 6:40 pm, WM <mueck...@rz.fh-augsburg.de> 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. > > > > B) There does not exist a natural number n such that P(n) is > > > false.
In fact we cannot find such a number. Nevertheless we cannot exclude its existence. Please consider what I wrote about the sets A and B. We cannot find a last finite number that has left A. Nevertheless it must exist. > > > In potential infinity you have to distinguish between existence and > > the possibility to identify. > > Every potentially infinite set of natural numbers has a last element. > > But you cannot identify it. > > I do not understand. You made the claim that A implies B.
For every number from 1 to n.
> Now you seem to be arguing against this. Note that the statement > in B is that the natural number n does not exist, not that > the natural number n cannot be identified. I remind you again > that the words are yours.-
The statement is that the natural number does not exist between 1 and n inclusively.
Find a FIS of d that is not in a line of the list or agree that you cannot prove that there is no natural number such that line(n) = d.