Mathematical axioms

thumb|The parallel postulate which states if the sum of the interior angles of two lines is less than 180°, the two straight lines meet on that side. The postulate is correct on a flat plane in [[Euclidean geometry but breaks on curved geometries such as spheres.]] An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.

axiomatic system for the natural numbers

axioms that are relevant to the probability theory

set of axioms from which some or all axioms can be used in conjunction to logically derive theorems

a formula in the metalanguage of an axiomatic system in which one or more schematic variables appear

property of certain mathematical objects (usually in a category) that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not probably exist.

rules related to the mathematical principles of origami

theorem

thesis in mathematical logic

properties that homology theories of topological spaces have in common

axioms in computational complexity theory

first-order axiomatization of a fragment of Euclidean geometry