# axiom

a self-evident truth that requires no proof.

a universally accepted principle or rule.

Logic, Mathematics. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.

## Origin of axiom

^{1}

## Words that may be confused with axiom

- 1. adage, aphorism, apothegm, axiom , maxim, proverb
- 2. assumption, axiom , premise, presumption

## Words Nearby axiom

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

## How to use axiom in a sentence

With an ATP, a programmer can code in all the rules, or axioms, and then ask if a particular conjecture follows those rules.

How Close Are Computers to Automating Mathematical Reasoning? | Stephen Ornes | August 27, 2020 | Quanta MagazineGödel’s main maneuver was to map statements about a system of axioms onto statements within the system — that is, onto statements about numbers.

By the first theorem, this set of axioms would then necessarily be incomplete.

We’ve learned that if a set of axioms is consistent, then it is incomplete.

It would mean that there exists a sequence of formulas built from these axioms that proves the formula that means, metamathematically, “This set of axioms is consistent.”

Whether or not Hippocrates ever actually said “First, do no harm,” the

*axiom*is central to medical ethics.Jakes says he believes in the

*axiom*that the act of forgiveness is not really a gift to others as much as it is a gift to oneself.Bishop T.D. Jakes on His New Book and Whitney Houston’s Death | Allison Samuels | March 10, 2012 | THE DAILY BEASTIt's Tip O'Neill's famous

*axiom*in reverse: now all politics is national.It is a generally accepted

*axiom*that a public man cannot afford to be modest in these go-ahead days of "boom."The Doctor of Pimlico | William Le QueuxThis truth is as old as Homer, and its proofs are as capable of demonstration as a mathematical

*axiom*.The Book of Anecdotes and Budget of Fun; | VariousBy this, OLeary understood that he was definitely adopted by virtue of the

*axiom*of what was his was theirs.The Woman Gives | Owen JohnsonThat was an

*axiom*on which was founded a vigorous war against all capillary adornments.The British Expedition to the Crimea | William Howard RussellHe starts with the

*axiom*that the whole amount of attention a reader can give at any moment is limited and fixed.English: Composition and Literature | W. F. (William Franklin) Webster

## British Dictionary definitions for axiom

/ (ˈæksɪəm) /

a generally accepted proposition or principle, sanctioned by experience; maxim

a universally established principle or law that is not a necessary truth: the axioms of politics

a self-evident statement

logic maths a statement or formula that is stipulated to be true for the purpose of a chain of reasoning: the foundation of a formal deductive system: Compare assumption (def. 4)

## Origin of axiom

^{1}

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Scientific definitions for axiom

[ ăk′sē-əm ]

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 © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## Cultural definitions for 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.

## Notes for axiom

The New Dictionary of Cultural Literacy, Third Edition Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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