axiom

IPA/ˈæksiəm/
KK[ˈæksiəm]IPA/ˈæksiəm/

axiom — noun

  • axiomsingular
  • axiomsplural

1. a short saying or rule that most people treat as obviously true and use as a sta

1.nounC1
Definition

a short saying or rule that most people treat as obviously true and use as a starting point when thinking or arguing about something.

Example

Grandma Rosa lived by the old axiom that honesty saves you trouble in the long run.

axiom that + clause stating the principle

Chef Lin reminded her students of the kitchen axiom that fresh ingredients matter more than fancy tools.

an axiom that + clause stating a field principle

Common collocations
  • old axiom
  • common axiom
  • popular axiom
  • live by an axiom
  • follow an axiom
  • reject an axiom
Synonyms
  • maxim

    more about rules for personal behaviour

  • adage

    an old, traditional saying passed down over time

  • truism

    often slightly negative — so obvious it adds little

  • principle

    broader; a basic rule guiding action or thought

Antonyms
  • fallacy

    a belief widely thought correct but actually wrong

Grammar Patterns

axiom that + clause

axiom of + noun

Usage Note

Subject is usually an idea or saying about life, work, or behaviour. Distinguish from sense 2: this sense names a popular belief, while sense 2 names a formal starting rule in maths or science.

Common Mistakes

I told my friend an axiom about the weather yesterday.
I shared an old saying about the weather with my friend.
'axiom' refers to a widely accepted general truth, not a casual remark or daily comment.

2. in maths, logic, or science, a basic rule that you agree to treat as true withou

2.nounC2
Definition

in maths, logic, or science, a basic rule that you agree to treat as true without proof, then use to build other rules and results from.

Example

Euclid built his geometry on five axioms about points, lines, and angles.

build [theory] on + axioms

Our teacher showed how every theorem in the chapter follows from three simple axioms.

follow from + axioms

Common collocations
  • fundamental axiom
  • mathematical axiom
  • axiom of choice
  • follow from an axiom
  • based on axioms
  • set of axioms
Synonyms
  • postulate

    near-identical in maths; chosen as a starting assumption

  • premise

    any starting statement in an argument, not only formal systems

  • first principle

    the most basic idea a field rests on, less technical

Antonyms
  • theorem

    a result proved from axioms, not assumed

Grammar Patterns

axiom of + field

from this axiom + clause

Usage Note

Almost always plural in real use ('the axioms of ...'). Distinguish from sense 1: here the rule is taken as true by formal agreement inside a system, not because most people believe it. Often paired with 'theorem', 'proof', or 'postulate'.

Common Mistakes

The teacher proved the axiom in front of the class.
The teacher proved a theorem using the axiom in front of the class.
axioms are accepted without proof; what gets proved from them is a theorem.

Word family

  • axiomatic
    adjectiveC2
  • axiomatically
    adverbC2

Synonym discussion

Sense: noun/1

All five words name short statements that people treat as true, but the flavour differs. An 'axiom' is presented as obviously or self-evidently true and is often used to start an argument or guide a field of thought. A 'maxim' focuses on rules for personal behaviour ('look before you leap'). An 'adage' is older and folk-flavoured, repeated across generations. A 'truism' carries a slightly tired tone — true but so obvious it teaches little. A 'principle' is the broadest of the group: any basic rule that guides decisions or design, not necessarily phrased as a saying. Compare: 'It is an axiom of teaching that students learn at different speeds' (presented as obvious starting truth), 'My grandfather's maxim was: never lend what you cannot afford to lose' (personal rule), and 'Honesty is the best policy' (a familiar adage).

axiom ↗maxim ↗adage ↗truism ↗principle ↗

Common collocations

Nouns

  • set of axioms
  • list of axioms
  • system of axioms

Phrases

  • follow from an axiom
  • based on the axiom that
  • live by the axiom that
  • challenge an axiom

Prepositions

  • axiom of
  • axiom about
  • axiom from

Etymology

GreekLatinMiddle FrenchEnglish

English picked up 'axiom' in the late 1400s from Middle French 'axiome', which came from Latin 'axioma'. The Latin word was borrowed from Greek 'axíōma', meaning 'something thought worthy or fit', built on the verb 'axioûn' ('to think worthy') and the adjective 'áxios' ('worthy, of like value'). The mathematical use — a starting rule taken as true without proof — grew out of this older sense of a statement considered worthy of belief on its own merit.