Meaning & use
axiom
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Meanings
nouncountablemathematics
A basic statement in logic or mathematics that is accepted as true and used as a starting point for further reasoning.
Grammar: Takes a plural: the axioms of geometry.
Patterns
- the axiom that something
- an axiom of something
Euclid built geometry on a short list of axioms.
One axiom states that a straight line joins any two points.
The proof depends on an axiom that cannot itself be proved.
nouncountable
A general principle or saying that people widely accept as true, even without testing it.
Grammar: Often followed by that: the axiom that practice makes perfect.
Patterns
- the axiom that something
- a basic axiom
It is an axiom of business that the customer comes first.
Many coaches follow the axiom that defense wins games.
The old axiom says that honesty is the best policy.
Word forms
| plural | axioms |
|---|
Common combinations
- basic axiom
- Equality is a basic axiom of the theory.
- accept an axiom
- You must accept the axiom before you can follow the proof.
- mathematical axiom
- A mathematical axiom needs no proof inside its system.
- axiom of choice
- The axiom of choice is a famous topic in set theory.
- economic axiom
- It is an economic axiom that people respond to incentives.
Synonyms and how they differ
- principle
- Principle is a broader word for a rule or belief, while axiom suggests an unproven starting point of a system.
- postulate
- Postulate is nearly the same but is often a claim assumed for an argument, while axiom feels more self-evident.
- maxim
- Maxim is a short saying giving practical advice, whereas an axiom is a statement taken as true.
- truism
- Truism is a statement so obvious it is almost pointless, while axiom is a serious foundation.
Opposites
Word family
- axiomatic adjective
- obviously true and not needing proof
- axiomatically adverb
- in a way that is accepted as true
- axiomatize verb
- to express a theory using axioms
- axiomatization noun
- the act of building a system from axioms
Commonly confused: axiom or theorem?
axiom vs theorem
A theorem is a statement that has been proved from axioms, whereas an axiom is assumed without proof.
Practice
In geometry, a statement accepted without proof and used to prove others is called a(n) ______.
Choose one answer.
An axiom is an unproven starting point. A theorem is proved from axioms, which is the tempting wrong answer.
Make it your own
Write a sentence using “axiom”, then check it and compare it with the examples above.