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. Although it was invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived.

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. In philosophy, sets are ordinarily considered to be abstract objects physically represented by groups of objects. For instance, three cups on a table when spoken of together as "the cups" form a set with three elements.

However, proponents of mathematical realism, including Penelope Maddy, have argued that sets are concrete objects. At the beginning of his Beiträge zur Begründung der transfiniten Mengenlehre, Georg Cantor, the principal creator of set theory, gave the following definition of a set:

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