In mathematics, a set is a collection of distinct objects. Each object, or element, can occur at most once. Ordering is not significant: sets do not impose any ordering on their elements.

Sets are usually named using capital letters, and brackets, {}, are used to enumerate a set’s elements. For example:

A = \{2, 5, 1, 3 \}
B = \{Homer, Marge, Bart, Lisa\}

Two sets are considered equal if and only if they contain exactly the same elements.


\in denotes set membership. i.e., 2 \in A. We can say that 2 is a member of A or 2 belongs to A. We can also say that A contains 2.

\notin means that an element is not a member of a set. 4 \notin A


Sets may be finite or infinite. \mathbb{R} is an example of an infinite set.

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