Philosophy, Philosophy Of Mathematics, Zenos Paradox, Real Number System, Dilemma.
arithmetic. Adding property (P13) uniquely determines the real numbers. (Smith, 2023, slightly modified) The challenge then is to prove that 999… satisfies each of the axioms, (A1) — (A13). The proof is easy enough for (A2), as 0 + 999…999 = 999… 999 + 0. Likewise, proofs can be readily given for