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set theory

n. (context mathematics English) The mathematical theory of sets.

set theory

n. the branch of pure mathematics that deals with the nature and relations of sets

Set theory

Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.

The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.

Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.

Set theory (music)

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen , drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.

One branch of musical set theory deals with collections ( sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.

Usage examples of "set theory".

I'm not familiar enough with autocatalytic set theory to understand the details, but it seems that a distinct phase transition is taking place.

The way we envision this new sort of senso-symphony, the artists--the mathists, that is--will transmogrify basic structures of thought, such as Euclidean conceptual edifices, or transfinite set theory fabrications.

Through set theory it was possible to introduce a beginner to mathematics, logic, electronics and all other fields of knowledge&mdash.

This was undecidable, within logically simpler systems like set theory.

This was undecidable, within logically simpler systems like set theory: additional assumptions had to be made.