Sinonimi & Anagrammi | Parola Inglese AXIOM

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Esempi di utilizzo di AXIOM in una frase

• In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty.
• An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
• In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A.
• This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member.
• Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced.
• Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an axiom.
• While the title states that the set theory presented is 'naive', which is usually taken to mean without formal axioms, the book does introduce a system of axioms equivalent to that of ZFC set theory except the Axiom of foundation.
• He is best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a Fields Medal.
• In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set.
• After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied.
• Like the other axioms of countability, separability is a "limitation on size", not necessarily in terms of cardinality (though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below) but in a more subtle topological sense.
• This work outlines key principles, including the axiom "Do what thou wilt shall be the whole of the Law," emphasizing personal freedom and the pursuit of one's true path, guided by love.
• In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic.
• The first three of these characterizations can be proven equivalent in Zermelo–Fraenkel set theory without the axiom of choice, but the equivalence of the third and fourth cannot be proved without additional choice principles.
• Ernst Zermelo introduced the axiom of choice as an "unobjectionable logical principle" to prove the well-ordering theorem.
• This theory, which is presently commonly accepted as a foundation of mathematics, contains the axiom of infinity, which means that the natural numbers form a set (necessarily infinite).
• By 1908, Russell arrived at a ramified theory of types together with an axiom of reducibility, both of which appeared in Whitehead and Russell's Principia Mathematica published in 1910, 1912, and 1913.
• An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures.
• The lemma was proved (assuming the axiom of choice) by Kazimierz Kuratowski in 1922 and independently by Max Zorn in 1935.
• The axiom of extensionality, also called the axiom of extent, is an axiom used in many forms of axiomatic set theory, such as Zermelo–Fraenkel set theory.

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