Синоними & Информация за | Английски дума AXIOMATIC

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Примери за използване на AXIOMATIC в изречение

• Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language.
• 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.
• Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today.
• These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events.
• 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.
• Z is based on the standard mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic.
• 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.
• In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory.
• In many popular versions of axiomatic set theory, the axiom schema of specification, subset axiom, axiom of class construction, or axiom schema of restricted comprehension is an axiom schema.
• In axiomatic set theory, the axiom of empty set, is a statement that asserts the existence of a set with no elements.
• In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory.
• In this book, Hawking and Ellis attempt to establish the axiomatic foundation for the geometry of four-dimensional spacetime as described by Albert Einstein's general theory of relativity and to derive its physical consequences for singularities, horizons, and causality.
• In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
• This allows an axiomatic construction of numbers and ordinal arithmetic, namely, the integers, reals, the countable infinity, and entire towers of infinite ordinals.
• Thus, for example, the studies of "hypercomplex numbers", such as considered by the Quaternion Society, were put onto an axiomatic footing as branches of ring theory (in this case, with the specific meaning of associative algebras over the field of complex numbers).
• An axiomatic system is called complete if for every statement, either itself or its negation is derivable from the system's axioms (equivalently, every statement is capable of being proven true or false).
• BAN logic uses postulates and definitions – like all axiomatic systems – to analyze authentication protocols.
• Its existence is unprovable in ZFC, the standard form of axiomatic set theory, but follows from a suitable large cardinal axiom.
• Musicologist Philip Tagg refers to the elitism associated with art music as one of an "axiomatic triangle consisting of 'folk', 'art' and 'popular' musics".

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