For questions on axioms, mathematical statements that are accepted as being true, usually without controversy.

An axiom is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy.

Axioms define and delimit the realm of analysis. In other words, an axiom is a formal statement that is assumed to be true. Therefore, its truth is taken for granted within the particular domain of analysis, and serves as a starting point for deducing and inferring other (theory and domain dependent) truths. An axiom is defined as a mathematical statement that is accepted as being true without a mathematical proof.

It should be mentioned that in modern times some statements receive a status of axioms, but they are still provable from weaker theories using other statements. One famous example is the **axiom** of choice, which is provable from ZF set theory if we assume Zorn's **lemma**. Generally, in modern foundations of mathematics, an axiom is just a statement in the base theory.