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

- mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements...
- In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented...
- 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...
- branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence...
- axiom Axiom of constructibility Rank-into-rank Kripke–Platek axioms Diamond principle Parallel postulate Birkhoff's axioms (4 axioms) Hilbert's axioms (20...
- axioms can be formulated which are logically equivalent to the parallel postulate (in the context of the other axioms). For example, Playfair's axiom...
- The Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central...
- not as an axiom but as a definition of equality. Then it is necessary to include the usual axioms of equality from predicate logic as axioms about this...
- 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...
- 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...