Definition:Axiom/Mathematics

Definition

The term axiom is used throughout the whole of mathematics to mean a statement which is accepted as true for that particular branch.

Different fields of mathematics usually have different sets of statements which are considered as being axiomatic.

So statements which are taken as axioms in one branch of mathematics may be theorems, or irrelevant, in others.

Also see

• Definition:Hilbert's Program
• Definition:Mathematical Logic

Linguistic Note

The usual plural form of axiom is axioms.

However, the form axiomata can also sometimes be found, although it is sometimes considered archaic.

Sources

• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.1$: The need for logic