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Biography. Badiou is the son of the mathematician Raymond Badiou [fr] (1905–1996), who was a working member of the Resistance in France during World War II. Alain Badiou was a student at the Lycée Louis-Le-Grand and then the École Normale Supérieure (1955–1960). [5] In 1960, he wrote his diplôme d'études supérieures [fr] (roughly ...
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole.
Zermelo–Fraenkel set theory. 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. Today, Zermelo–Fraenkel set theory, with the ...
Method. A naive theory in the sense of "naive set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and operations on sets. Such theory treats sets as platonic absolute objects. The words and, or, if ... then, not, for some, for every are treated as in ordinary mathematics.
t. e. In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician Bertrand Russell in 1901. [1][2] Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. [3]
Von Neumann–Bernays–Gödel set theory. In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range ...
In Zermelo–Fraenkel (ZF) set theory, the natural numbers are defined recursively by letting 0 = {} be the empty set and n + 1 (the successor function) = n ∪ {n} for each n. In this way n = {0, 1, …, n − 1} for each natural number n. This definition has the property that n is a set with n elements. The first few numbers defined this way ...
The fundamental concept of musical set theory is the (musical) set, which is an unordered collection of pitch classes. [4] More exactly, a pitch-class set is a numerical representation consisting of distinct integers (i.e., without duplicates). [5] The elements of a set may be manifested in music as simultaneous chords, successive tones (as in ...