# axiom

/ˈæksiəm/ (US) · /ˈæksɪəm/ (UK) · CEFR C1 · Noun

Source: https://englishreference.com/word/axiom
Updated: 2026-05-11

## Definition

a rule or statement that everyone accepts as true without needing proof. It is the starting point for a bigger idea or a system of math.

For teachers: a self-evident truth that requires no proof to be accepted; a starting proposition in a logical system from which other truths are derived.

## Examples

- It is a mathematical axiom that the whole is greater than the part.
- The entire legal argument was built upon the axiom that all citizens deserve equal protection under the law.
- In Euclidean geometry, the parallel postulate was long considered an unshakeable axiom until the development of non-Euclidean systems challenged its universal necessity.

## Usage notes

- Often used in formal logic, mathematics, and philosophy to describe foundational principles.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.