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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.

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.

- 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...

- 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...

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