Definition of Axioms. Meaning of Axioms. Synonyms of Axioms

Here you will find one or more explanations in English for the word Axioms. Also in the bottom left of the page several parts of wikipedia pages related to the word Axioms and, of course, Axioms synonyms and on the right images related to the word Axioms.

Definition of Axioms

Axiom
Axiom Ax"i*om, n. [L. axioma, Gr. ? that which is thought worthy, that which is assumed, a basis of demonstration, a principle, fr. ? to think worthy, fr. ? worthy, weighing as much as; cf. ? to lead, drive, also to weigh so much: cf F. axiome. See Agent, a.] 1. (Logic & Math.) 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.' 2. An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy. Syn: Axiom, Maxim, Aphorism, Adage. Usage: An axiom is a self-evident truth which is taken for granted as the basis of reasoning. A maxim is a guiding principle sanctioned by experience, and relating especially to the practical concerns of life. An aphorism is a short sentence pithily expressing some valuable and general truth or sentiment. An adage is a saying of long-established authority and of universal application.

Meaning of Axioms from wikipedia

- arithmetic. Non-logical axioms may also be called "postulates", "****umptions" or "proper axioms". In most cases, a non-logical axiom is simply a formal logical...
- mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...
- the axioms of Zermelo–Fraenkel set theory. Most of the axioms state the existence of particular sets defined from other sets. For example, the axiom of...
- axioms can be formulated which are logically equivalent to the parallel postulate (in the context of the other axioms). For example, Playfair's axiom...
- probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central...
- the axiom of choice for their proofs. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, such as the axiom of...
- axiom Axiom of constructibility Rank-into-rank Kripke–Platek axioms Diamond principle Parallel postulate Birkhoff's axioms (4 axioms) Hilbert's axioms (20...
- These axioms were also modified by the School Mathematics Study Group to provide a new standard for teaching high school geometry, known as SMSG axioms. A...
- the Peano axioms and finite sets; Kripke–Platek set theory, which omits the axioms of infinity, powerset, and choice, and weakens the axiom schemata of...
- record producer Axioms (album), a 1999 album by Asia Axiom (computer algebra system), a free, general-purpose computer algebra system AXIOM (camera), a professional...