Reference
In mathematics, a set is a collection of distinct elements. The elements that make up a set can be any kind of things: people, letters of the alphabet, numbers, points in space, lines, other geometrical shapes, variables, or even other sets.[4] Two sets are equal if and only if they have precisely the same elements.
Sets are ubiquitous in modern mathematics. The subject called set theory is part of the foundations of mathematics.
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The foremost property of a set is that it can have elements, also called members. Two sets are equal if and only if every element of each set is an element of the other; this property is called the extensionality of sets.
The simple concept of a set has proved enormously useful in mathematics, but paradoxes arise if no restrictions are placed on how sets can be constructed:
Russell's paradox shows that the "set of all sets that do not contain themselves", i.e., {x | x is a set and x ? x}, cannot exist.
Cantor's paradox shows that "the set of all sets" cannot exist.
Naïve set theory defines a set as any well-defined collection of distinct elements, but problems arise from the vagueness of the term well-defined.
https://en.wikipedia.org/wiki/Set_(mathematics)
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