# Definition:Axiom/Mathematics

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## 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.

It is possible (and this is the ultimate aim of $\mathsf{Pr} \infty \mathsf{fWiki}$) to justify basing the whole of mathematics on a handful of axioms.

## Sources

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