Axiom - Wikipedia
In the field of mathematical logic, a clear distinction is made between two notions of axioms: logical and non-logical (somewhat similar to the ancient distinction between "axioms" and "postulates" respectively).

AXIOM Definition & Meaning - Merriam-Webster
In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom.

List of axioms - Wikipedia
In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system. Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory.

Axioms | Open Access Journal | MDPI
Axioms is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published monthly online by MDPI.

AXIOM | English meaning - Cambridge Dictionary
AXIOM definition: 1. a statement or principle that is generally accepted to be true, but need not be so: 2. a formal…. Learn more.

AXIOM Definition & Meaning | Dictionary.com
In mathematics, a statement that is unproved but accepted as a basis for other statements, usually because it seems so obvious. The term axiomatic is used generally to refer to a statement so obvious that it needs no proof.

Axiom - Simple English Wikipedia, the free encyclopedia
It is a statement which is assumed to be true without question, and which does not require proof. It is also known as a postulate (as in the parallel postulate). [1] . The axiom is to be used as the premise or starting point for further reasoning or arguments, [2] usually in logic or in mathematics. [3][4]

10.2: Axioms, Theorems, and Proofs - Mathematics LibreTexts
There is a strange creature in mathematics, not typically mentioned in lower division texts, called an axiom (or, in some texts, a postulate). An axiom is a self-evident or universally recognized truth. It is accepted as true, without proof, as the basis for argument.

Axiom | Logic, Mathematics, Philosophy | Britannica
Some recommend that the term axiom be reserved for the axioms of logic and postulate for those assumptions or first principles beyond the principles of logic by which a particular mathematical discipline is defined.

2.1: Axioms and Basic Definitions - Mathematics LibreTexts
Observe that the axioms only state certain properties of real numbers without specifying what these numbers are. Thus we may treat the reals as just any mathematical objects satisfying our axioms, but otherwise arbitrary.