> 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). (2) exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k. (2) is in contradiction with (1).
Try to explain the matheological conditions other than by (1) and (2).