An axiom of a mathematical system is a statement that is assumed to be true. No proof is given. From axioms we derive propositions and theorems.

Axioms are sometimes described as self-evident, though many are not, and are defining properties of mathematical systems. Induction is one such axiom, taken as a defining property of .

Just a handful of axioms, called the Zermelo-Fraenkel with Choice axioms(ZFC), together with a few logical deduction rules, appear to be sufficient to derive essentially all of mathematics. However, for practical purposes, they are much too primitive.