axiom (Meaning)
axiom (n)
a saying that is widely accepted on its own merits
(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
axiom (a.)
A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, The whole is greater than a part; A thing can not, at the same time, be and not be.
An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.
Synonyms & Antonyms of axiom
axiom Sentence Examples
- The Euclidean axiom states that a straight line can be drawn between any two points.
- The axiom of choice asserts that for any collection of non-empty sets, there exists a function that selects an element from each set.
- By the axiom of substitution, if two propositions are equivalent, then one can be used to replace the other in any argument.
- The Zermelo-Fraenkel axiom system is the foundation for most modern set theory.
- The three axioms of probability theory are the axioms of addition, multiplication, and inclusion-exclusion.
- The axiom of extensionality states that two sets are equal if and only if they have the same elements.
- The Peano axioms are the basic axioms for arithmetic.
- The Zermelo-Fraenkel-Choice axiom system is a commonly used foundation for mathematics.
- The Riemann hypothesis is an unproven axiom that predicts the distribution of the Riemann zeros.
- The axiom of completeness states that for any set of real numbers that has an upper bound, there exists a least upper bound.
FAQs About the word axiom
a saying that is widely accepted on its own merits, (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evidentA
principle, doctrine, law,theory, tenet, hypothetical, thesis, standard, premise, premiss
No antonyms found.
The Euclidean axiom states that a straight line can be drawn between any two points.
The axiom of choice asserts that for any collection of non-empty sets, there exists a function that selects an element from each set.
By the axiom of substitution, if two propositions are equivalent, then one can be used to replace the other in any argument.
The Zermelo-Fraenkel axiom system is the foundation for most modern set theory.
