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ax⋅i⋅om

  [ak-see-uhm]
Use axiom in a Sentence
–noun
1. a self-evident truth that requires no proof.
2. a universally accepted principle or rule.
3. Logic, Mathematics. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
Origin:
1475–85; < L axiōma < Gk: something worthy, equiv. to axiō-, var. s. of axioûn to reckon worthy + -ma resultative n. suffix
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
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ax·i·om   (āk'sē-əm)   
n.  
  1. A self-evident or universally recognized truth; a maxim: "It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services" (Albert Jay Nock).
  2. An established rule, principle, or law.
  3. A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.

[Middle English, from Old French axiome, from Latin axiōma, axiōmat-, from Greek, from axios, worthy; see ag- in Indo-European roots.]
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Axiom

Ax"i*om\, n. [L. axioma, Gr. ? that which is thought worthy, that which is assumed, a basis of demonstration, a principle, fr. ? to think worthy, fr. ? worthy, weighing as much as; cf. ? to lead, drive, also to weigh so much: cf F. axiome. See Agent, a.]

1. (Logic & Math.) 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."

2. An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.

Syn: Axiom, Maxim, Aphorism, Adage.

Usage: An axiom is a self-evident truth which is taken for granted as the basis of reasoning. A maxim is a guiding principle sanctioned by experience, and relating especially to the practical concerns of life. An aphorism is a short sentence pithily expressing some valuable and general truth or sentiment. An adage is a saying of long-established authority and of universal application.
Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
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Language Translation for : axiom
Spanish: axioma,
German: das Axiom,
Japanese: 公理
More Translations »

axiom [(ak-see-uhm)]

In mathematics, a statement that is unproved but accepted as a basis for other statements, usually because it seems so obvious.

Note: The term axiomatic is used generally to refer to a statement so obvious that it needs no proof.
The American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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axiom 
1485, from M.Fr. axiome, from L. axioma, from Gk. axioma "authority," lit. "that which is thought worthy or fit," from axioun "to think worthy," from axios "worthy, worth, of like value, weighing as much," from PIE adj. *ag-ty-o- "weighty," from base *ag- "to drive, draw, move" (cf. Gk. agein "weigh, pull").
Online Etymology Dictionary, © 2001 Douglas Harper
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axiom   (āk'sē-əm)  Pronunciation Key 
A principle that is accepted as true without proof. The statement "For every two points P and Q there is a unique line that contains both P and Q" is an axiom because no other information is given about points or lines, and therefore it cannot be proven. Also called postulate.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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AXIOM language
A commercially available subset of Scratchpad, from IBM.
["Axiom - The Scientific Computing System", R. Jenks et al, Springer 1992].
(1995-02-21)

axiom logic
A well-formed formula which is taken to be true without proof in the construction of a theory.
Compare: lemma.
(1995-03-31)

The Free On-line Dictionary of Computing, © 1993-2007 Denis Howe
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