Philosophy, Philosophy Of Mathematics, Zenos Paradox, Real Number System, Dilemma.
suppose there were a proof that 999… did violate one of more of the axioms (A1) to (A13). This as well would not show that 999… is not a real number. The violation of the axioms would not be surprising since 999… is essentially an inconsistent number, as postulated by Priest (Priest, 1994). And, in