General Mathematics

    

Uf0: τ(0)⊕0=τ(1)⊕1 a One-Line Axiomatization of the Birth and Dissolution of Mathematics

Authors: Kleschev Anton Alevtinowitch

We present UF0(Unified Foundation 0), a minimal formal system in which the entire edificeof natural-number arithmetic is generated and dissolved by a single equation. u2022 0 is the pre-numerical, non-dual point. u2022 τ is a unary "tear" operator enacting the primal split. u2022 ⊕ is a non-repeating union. The sole axiom τ (0) ⊕ 0 = τ (1) ⊕ 1 simultaneously encodes 1. the birth of mathematics (0 → 1), and 2. the fundamental duality (1 → 2), while collapsing both into identity when 0 = 1 = 2. No external arithmetic, set theory, or category theory is presupposed. UF0 is therefore the first fully formal, one-sentence foundation that captures both the emergence and the illusoriness of number.

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[v1] 2025-07-15 19:10:04

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