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A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.




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Definition
Georg Cantor, the founder of set theory, gave the following definition of a set at the beginning of his Beitr√§ge zur Begr√ľndung der transfiniten Mengenlehre:
Sets are conventionally denoted with capital letters. Sets A and B are equal if and only if they have precisely the same elements.
As discussed below, the definition given above turned out to be inadequate for formal mathematics; instead, the notion of a "set" is taken as an undefined primitive in axiomatic set theory, and its properties are defined by the Zermelo–Fraenkel axioms.
The most basic properties are that a set "has" elements, and that two sets are equal (one and the same) if and only if they have the same elements.

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