axioms

n. premise, basic assumption, truism, recognized truth

This article is about a logical statement. For the vehicle, see Isuzu Axiom. For other uses, see Axiom (disambiguation)An axiom is a sentence or proposition that is not proved or demonstrated and is considered as self-evident or as an initial necessary consensus for a theory building or acceptation. Therefore, it is taken for granted as true, and serves as a starting point for deducing and inferencing other (theory dependent) truths. In mathematics, an axiom is any starting assumption from which other statements are logically derived. It can be a sentence, a proposition, a statement or a rule that enables the construction of a formal system. Unlike theorems, axioms cannot be derived by principles of deduction, nor are they demonstrable by formal proofs—simply because they are starting assumptions—there is nothing else they logically follow from (otherwise they would be called theorems). In many contexts, "axiom," "postulate," and "assumption" are used interchangeably.
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Axiom is a computer algebra system. It is useful for research and development of mathematical algorithms for which it defines a strongly typed, mathematically correct type hierarchy. i.e., mathematical objects (such as rings, fields, polynomials) as well as data structures from computer science (e.g., lists, trees, hash tables) are automatically typed. When an operation is applied to an object the type of the object determines the behaviour of the operation (similar to OOP).
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Noun
1. a saying that widely accepted on its own merits
(synonym) maxim
(hypernym) saying, expression, locution
(hyponym) aphorism, apothegm, apophthegm
2. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
(hypernym) proposition
(classification) logic

<language> A commercially available subset of Scratchpad, from IBM.
["Axiom - The Scientific Computing System", R. Jenks et al, Springer 1992].
(1995-02-21)

<logic> A well-formed formula which is taken to be true without proof in the construction of a theory.
Compare: lemma.
(1995-03-31)

ASSIOMI