Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A selfevident 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).
 n. An established rule, principle, or law.
 n. A selfevident principle or one that is accepted as true without proof as the basis for argument; a postulate.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A seemingly selfevident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
 n. 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".
 n. An established principle in some artistic practice or science that is universally received.
from the GNU version of the Collaborative International Dictionary of English
 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.”
 n. An established principle in some art or science, which, though not a necessary truth, is universally received.
from The Century Dictionary and Cyclopedia
 n. A selfevident, undemonstrable, theoretical, and general proposition to which every one who apprehends its meaning must assent.
 n. Any higher proposition, obtained by generalization and induction from the observation of individual instances; the enunciation of a general fact; an empirical law.
 n. In logic, a proposition, whether true or false: a use of the term which originated with Zeno the Stoic.
 n. one of those generalizations of ordinary experience which nobody doubts, and which are soon replaced by scientific formulations, which latter are also, but less properly, termed middle axioms.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be selfevident
 n. a saying that is widely accepted on its own merits
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

Use of the term axiom reinforces that our computational model is a mathematical, formal system and that analogue execution is a form of deduction from the axioms or assumptions explicitly programmed into the model.

Although he lacks the historical context to articulate Kant's Categorical Moral Imperative, he describes a Supreme Being for whom something akin to this axiom is the ultimate measure of a man, a God who believes that one's ethical duty is to acquire and exercise wisdom, to evaluate and constantly reevaluate one's beliefs  including what one's ethical duty is  by applying the utmost objectivity to one's own preconceptions and prejudices.

So if the math relates to a physics matter the "axiom" is tested.

That simple axiom is a radical critique of an age in which ideological lines are hardening and real dialogue diminishing in the public arena.

It seems the operating axiom is the old "When all else fails, do what's right."

That axiom is also true in fantasy baseball, where managing a pitching staff down the stretch is often the key to winning a championship because major league teams often don't have the same agendas for their pitchers as fantasy owners do.

No, the axiom is concerned with the morality of genocide.

It will remain logically possible that the [progenocidal] axiom is objectively correct.

It will remain logically possible that the axiom is objectively correct.

To ignore such sources would be, among other things, to ignore the main axiom of historical research: Use all sources possible but treat none uncritically.
'I Saw a Nightmare …' Doing Violence to Memory: The Soweto Uprising, June 16, 1976
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