# 2.1Basic Operations of Sets

## 2.1.1 Sets and Membership

Sets are (arguably) the most fundamental of all mathematical objects. Quite simply, a set is

a collection things, the things belonging to the set are called members

or elements of the set.^{1} Other synonyms for the word “set,” are *collection*, *class, family*, and *ensemble*. We refer to a collection of people, family of functions, an ensemble of voters, and so on. We even consider sets whose members themselves are sets, such as the set of classes at a university, where each class consists of students. In mathematics, we might consider the set of all open intervals on the real line or the set of solutions of an equation.

If a set does not contain too many members, we can specify the set by simply writing down the members of the inside a pair of brackets, such as {3, 7, 31}, which denotes the first three Mersenne primes.^{2} Sometimes sets contain an infinite number of elements, like the natural numbers, where we might specify them by {1, 2, 3, …}, where the three dots after the 3 signify “and so on.”

We generally denote sets by capital letters such as *A*, *B*, *C*, … and members of sets by small letters, ...

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