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axiom Definition

axi·om (ak′sē əm)

noun

  1. a statement universally accepted as true; maxim
  2. an established principle or law of a science, art, etc.
  3. Logic, Math. a statement or proposition that needs no proof because its truth is obvious, or one that is accepted as true without proof Euclid's axiom that things equal to the same thing are equal to each other

Etymology: Fr axiome < L axioma < Gr axiōma, authority, authoritative sentence < axioun, to think worthy < axios, worthy < base of agein, to weigh, orig., to lend: see act

axiom Synonyms

axiom

n.

  1. A maxim

    maxim, saying, adage, aphorism; see proverb.

  2. A proposition assumed to be true

    premise, assumption, postulate; see hypothesis.

axiom Usage Examples

Preposition: of

  • extensionality: Axiom of extensionality: Classes with the same elements are the same.
  • infinity: What about the axiom of infinity - that there is an infinite set?
  • geometry: For more than two thousand years, the axioms of Euclidean geometry, were considered to be self evident.
  • logic: Although he works with logic and proofs every day as a mathematician, he questions whether our axioms of logic are fundamental.
  • choice: Did the paradoxes come from the ' Axiom of choice ' ?
  • theory: The axioms of set theory, in contrast, do not have such a variety of models.

Converse of object

  • satisfy: It will satisfy Infinity and Choice if the original model of TST satisfies these axioms.
  • add: SDL can be strengthened in various ways, in particular, we might consider adding axioms where deontic operators are embedded within one another.
  • apply: In order to apply the axiom of separation, we need to have some sets A from which to carve out subsets using properties.
  • follow: The real reason for Dell's success is that the company follows a fundamental axiom: don't do anything stupid.

Adjective modifier

  • Hermetic: We give below some of the more important Hermetic Axioms from The Kybalion with a few comments added to each.
  • logical: The domain model and scenario induce a set of logical axioms.
  • fifth: It is Cordemoy's fourth and fifth axioms which, together with this conclusion, get us occasionalism.
  • fundamental: The real reason for Dell's success is that the company follows a fundamental axiom: don't do anything stupid.
  • parallel: Alternative ( a ) was Euclid's parallel axiom.
  • basic: It must be treated as the basic axiom, since soil behavior is governed by it.

Modifies a noun

  • schema: Both calculi are characterized by a relatively larger number of deduction rules and a simple axiom schema.

Noun used with modifier

  • comprehension: The most general comprehension axiom of Z is the axiom of Separation.
  • domain: As noted earlier, the appropriateness of the rigged Hilbert space framework enters by way of the domain axiom.
  • action: According to Mises, all of the categories, theorems, or laws of economics are implied in the action axiom.
axiom Quotes

It is an axiom enforced by all the experience of the ages, that they who rule industrially will rule politically.

—Connolly,James

Axiome: la haine du bourgeois est le commencement de la vertu. Axiom: Hatred of the bourgeois is the beginning of wisdom.

—Flaubert, Gustave

C'est un axiome de la science politique aux EŁ  tats-Unis, que le seul moyen de neutraliser les effets des journaux est d'en multiplier le nombre. It isanaxiomof politicsinthe United States, thatthe only means of neutralising the effects of newspapers is to increase their number.

—Tocqueville, Alexis Charles Henri Cle¤  rel de

It is an axiom of sports that the legs go first. For sportswriters, it's the enthusiasm.

—Frayne,Trent

It has long beenanaxiomof minethatthe littlethings are infinitely the most important.

—Doyle, SirArthur Conan

All the nice people were poor; at least, that was a general axiom, the best of the rich being poor in spirit.

—Spark, Dame Muriel Sarah ne¤  e  Camberg