
Definition of Axiom
1. Noun. A saying that is widely accepted on its own merits.
Generic synonyms: Expression, Locution, Saying
Specialized synonyms: Aphorism, Apophthegm, Apothegm, Gnome, Moralism
Derivative terms: Axiomatic
2. Noun. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be selfevident.
Category relationships: Logic
Generic synonyms: Proposition
Derivative terms: Axiomatic, Axiomatic, Axiomatical
Definition of Axiom
1. n. A selfevident 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."
Definition of Axiom
1. Noun. (philosophy) A seemingly (selfevident) or necessary (truth) which is based on (assumption); a (principle) or (proposition) which cannot actually be proven or dis?proven. ¹
2. Noun. (mathematics logic) A fundamental (theorem) that serves as a basis for (deduction) of other theorems. Examples: "Through a pair of distinct points there passes exactly one straight line", "All right angles are congruent". ¹
3. Noun. An established principle in some artistic practice or science that is universally received. ¹
¹ Source: wiktionary.com
Definition of Axiom
1. a selfevident truth [n S]
Medical Definition of Axiom
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Axiom Pictures
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Lexicographical Neighbors of Axiom
Literary usage of Axiom
Below you will find example usage of this term as found in modern and/or classical literature:
1. American Journal of Mathematics by Johns Hopkins University, American Mathematical Society (1919)
"axiom 1. axiom 2. subset of K. §3. The axioms of S. There exists at least one
region. If R and K are regions and R' is a subset of K' then R is a axiom 3. ..."
2. History of English Literature by Hippolyte Taine (1897)
"In the first we merely remark that the contrary of the axiom is ... Having given
the definition of the straight line, we find that the axiom that two ..."
3. The Foundations of Geometry by David Hilbert (1902)
"axiom OF PARALLELS. (EUCLID'S axiom.) . The introduction of this axiom simplifies
greatly the fundamental principles of geometry and facilitates in no ..."
4. Geometry of Riemannian Spaces by Élie ( Cartan (1983)
"We shall say that a Riemannian space satisfies the axiom of the Plane if it ...
Later we shall determine every Riemannian space satisfying the axiom of the ..."
5. The Mechanical Theory of Heat: With Its Applications to the Steamengine and by Rudolf Clausius (1867)
"I cannot but• think, however, that his objection arises from an incorrect
interpretation of my axiom, a misconception which certainly might easily be formed ..."
6. The Philosophy of the Inductive Sciences: Founded Upon Their History by William Whewell (1847)
"It would seem more natural to say, if the former axiom is a definition of the
word equal, that the latter is a definition of the word greater. ..."
7. Proceedings of the London Mathematical Society by London Mathematical Society (1907)
"This is equivalent to Zermelo's axiom,* and it is not, so far as I know, a necessary
... Zermelo's axiom is a generalized form of the multiplicative axiom, ..."