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* the set of all words over <math>{a, b}\,</math> * the set <math>\left \{ a^{n}\right\}</math>, where <math>n\,</math> is a [[natural ...

...set definition of Georg Cantor.png|thumb|Cantor's original definition of a set: ''By an aggregate (..) we are to understand any collection into a whole (. ...Anything'' can be a member of a set. A set can be a member of a set. (If a set is a member of itself, '''beware''' of [[Russell's paradox]].) ...

...''') is a concept from [[mathematics]]. In many ways, multisets are like [[set]]s. Certain items are either elements of that multiset, or they are not. Ho ...me]] factors of a number ''n''. Here the underlying set of elements is the set of prime [[divisor]]s of ''n''. For example the number ''120'' has the [[fa ...

...h theory]] a '''graph''' is used to represent the connection between two [[set]]s. One of the sets contains nodes (which are officially called '''vertices ...t, where an edge that connects to the vertex at both ends (a [[loop (graph theory)|loop]]) is counted twice. ...

..."traditional" or "economic" [[game theory]]. CGT arose in relation to the theory of impartial games, the two-player game of [[Nim]] in particular, with an e Combinatorial Game Theory is largely confined to the study of a subset of combinatorial games which a ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one *<math>\Omega</math> is a set, called the '''sample space'''. ...

* 概率论（Probability Theory） * [[组合数学 (Fall 2024)/Problem Set 1|Problem Set 1]] [[组合数学 (Spring 2024)/第一次作业提交名单|第一次作业提交名单]] ...

:''This article is about the basic notions. For advanced topics, see [[Group theory]].'' ...ake a third element, also in the set. A familiar example of a group is the set of [[integer]]s together with the [[addition]] operator. ...

A '''time signature''' is a set of two [[numbers]], one on top of the other one, written right after the [[ {{music theory}} ...

...equations are called [[wikt:equivalent|equivalent]] if they have the same set of [[Algebraic solutions|solutions]]. This means that all solutions of the ...'''. When solving an equation, we need to say in which [[Set (mathematics)|set]] the solutions are allowed. For example, for an equation over the rational ...

...real number can simply be written as <math>a + 0 \cdot i</math> or as the set {{math|(''a'', 0)}}.<ref name="wa" /> The set of all complex numbers is usually written as <math>\mathbb{C}</math>. ...

Usually the input "data stream" is from a massive data set (e.g. search engine data), so you cannot afford storing the entire input. M (Interviewing problem of Theory Group in Microsoft Research Asia for student interns.) ...

In formal [[number theory]] a '''Gödel numbering''' is a [[function (mathematics)|function]] which as ...equivalence theorem]] states criteria for which those numberings of the set of computable functions are Gödel numberings. ...

== Assumption throughout Problem Set 3== == Problem 3 (Probability meets graph theory) == ...

| rowspan=2|[[set theory|set membership]] | a∈S means that a is an element of the set S ...

...osure of [[intersection]]. Open sets have infinite closure of [[union (set theory)|union]]. That is, in mathematical notation, if A₀, and A<sub>1< ...

...a [[coordinate system]]. This means that every place can be specified by a set of three numbers, called coordinates. ...ne by the Babylonians; Ancient Greeks, like [[Ptolemy]] later extended the theory. ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one *<math>\Omega</math> is a set, called the '''sample space'''. ...

<math>\mathbf{Z}</math> or <math>\mathbb{Z}</math> is the name of the [[set]] of integers. (<math>\mathbf{Z}</math>, +, 0) is an [[abelian group]]. [[Category:Number theory]] ...

...ht, "Chromatic Features of E♭-Major Works of the Classical Period" ''Music Theory Spectrum'' '''22''' 2 (2000): 178</ref> ...t to A and E a [[perfect fifth|fifth]] apart. In most other keys, they are set a [[perfect fourth|fourth]] apart. ...