noun

axiom

AK-see-uhm

Axiom (noun) means a statement accepted as true without proof, used as a starting point from which other results are derived. Example: “Euclid built his geometry on five axioms.”

noun

A statement accepted as true without proof, used as a starting point from which other results are derived.

"Euclid built his geometry on five axioms."

"If you change one axiom, the whole system that follows it changes with it."

A saying or principle that is widely regarded as obviously true.

"He lived by the old axiom that you should never lend what you cannot afford to lose."

"It is an axiom of the trade that the last ten per cent takes the longest."

How to Use Axiom

Learner’s notes

In plain EnglishSomething taken as true from the start, without needing proof.

When to use it

Formal. The mathematical sense is technical and precise; the everyday sense is closer to a well-worn saying. The adjective is axiomatic.

Memory tip

An axiom is assumed; a theorem is proved from axioms. If someone asks you to demonstrate an axiom, you have misidentified it.

Trace the full origin ↓

Easily confused with

theorem → postulate adage → maxim → hypothesis →

Common pairings

basic axiom axiom of choice self-evident axiom it is an axiom that

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Fill the Gap

Can you complete this real example?

Euclid built his geometry on five _____.

Etymology

From Greek axioma 'that which is thought worthy or self-evident', from axios 'worthy'.

Origin: Greek

Synonyms

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postulate premise first principle given maxim adage truism precept

Antonyms

theorem conclusion

Related Words

end law given saying decision particular beginning basis

Rhymes for axiom

idiom

See all rhymes for axiom →

Frequently Asked Questions

What is the difference between an axiom and a theorem?

An axiom is assumed without proof and forms the foundation of a system. A theorem is a statement proved by reasoning from the axioms. Mathematics works by keeping the axioms few and explicit, then deriving as much as possible from them.

What is the difference between an axiom and a hypothesis?

An axiom is adopted as a fixed starting point and is not tested within the system that uses it. A hypothesis is a provisional claim put forward precisely so it can be tested and possibly rejected.

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