Axiom

usgb/ˈæksiəm/
noun

A statement that is accepted as true without proof.

The idea that 'things equal to the same thing are equal to each other' is an axiom used in mathematics.
Visual representation of "axiom" - A statement that is accepted as true without proof.

Often appears as...

  • mathematical axiom
  • self-evident axiom

Usage tips

Academic

Definition 1 of 2
Visual representation of "axiom"
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Unquestioned Premise

In logic or math, an axiom is a starting point for reasoning, not questioned or tested.

Illustration for Unquestioned Premise
In geometry, the axiom that parallel lines never intersect is a given.
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Foundational Importance

Axioms form the foundation of logical arguments or mathematical proofs.

Illustration for Foundational Importance
He used the axiom of symmetry as the base for his theorem.
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Not a Proof

An axiom shouldn't be confused with a theorem, which is proven based on axioms and definitions.

Illustration for Not a Proof
The professor stated the axiom clearly, without offering a proof.
Visual representation of the word "Axiom"

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