# axiom

In formal mathematics an axiom is a formula or schema of formulas that is stipulated as true (and therefore not requiring proof). Axioms are the counterpart in mathematics of suppositions, assumptions, or premises in ordinary syllogistic logic.

A mathematical *theory* may be understood as consisting of all of the statements that may be derived from its axioms. For example, Euclidean-geometry is based on Euclid’s well-known five axioms (typically called *postulates* in geometry), and common set theory is usually taken as the theory of the Zermelo-Fränkel axioms.

- [MLA] “axiom.”
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 21 Feb 2013. Web. 21 Feb 2013. <http://platonicrealms.com/> - [APA] axiom (21 Feb 2013). Retrieved 21 Feb 2013 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/axiom/