In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 20 Apr., 19:23, fom <fomJ...@nyms.net> wrote: > > > Then it is certainly within your power to formulate > > different definitions, present them for consideration, > > and use them to prove an inconsistency. > > > > Until then, an inconsistency is established when > > legitimate proof methods yield proofs for a given > > statement as well as that statement's negation. > > And if a contradiction occurs, the method was not legitimate. > That need not be substantiated but follows from the fact of > contradiction. > > (1) forall n, forall i : (n < i <==> ~(n e s_i)) & (n >= i <==> n e > s_i).
WM's (1) is false, since "An, Ai, n < i <==> (n e s_i)" is true
So his other claims are irrelevant.
One can also note that "(n >= i <==> n e s_i)" is also false.
So it seems that WM's mathematical incapacity to create true arguments remain with him. --