## Sets

**Definition**

A **set** is a collection of explicitly-defined distinct *elements*.

**Elements of a Set**

If 2, 4, 6, 8 are elements of *A*, we can then write

$A = \{0, ~ 2, ~ 4, ~ 6, ~ 8\}$

or it can be written using the **set-builder** notation

$A = \{x ~ : ~ x \text{ is an even digit} \}$

read as "*A* is the set of all *x* such that *x* is an even digit".

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