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Definition: Sets are not given a formal definition. The are collections of things, or lists of things, in which nothing is repeated.

There are two notations for sets.

Order does not matter, so \(\{1, 2, 3, 4\} = \{4, 2, 1, 3\}\)

Elements cannot be repeated, so \(\{1, 1, 2\}\) is not a set.

Sometimes sets are defined by description. For example, let \(S\) be the set of all people who live in Iowa, or let \(B\) be the set of all black holes. Although I can't list all of the elements in the sets or find a pattern to describe the sets, I can tell you whether something is an element of the set or not.

You can think of the set \(A\) as the red circle.

A 7 5 1 2 8 3 4
The set \(A\) is the set of points \(\{1, 5, 7\}\).