1. axiom - Noun
2. axiom - Adjective
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."
An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.
Source: Webster's dictionaryAbout his model Fernandez has been known to comment, "Soy de aquí como el coquí" (I'm as Puerto Rican as a coquí), a common patriotic axiom. Source: Internet
A formulation of set theory that does not include the axiom of replacement will likely include some form of the axiom of separation, to ensure that its models contain a sufficiently rich collection of sets. Source: Internet
After that step, the axiom of choice is not used again. Source: Internet
A function f has a right inverse if and only if it is surjective (though constructing such an inverse in general requires the axiom of choice ). Source: Internet
Also Wacław Sierpiński proved that ZF + GCH (the generalized continuum hypothesis ) imply the axiom of choice and hence a well order of the reals. Source: Internet
Although the axiom of constructibility does resolve CH, it is not generally considered to be intuitively true any more than CH is generally considered to be false (Kunen 1980, p. 171). Source: Internet