Easy# Set Notation, Element of a Set

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In mathematics, we usually use *set notation* to describe properties satisfied by the elements of a set and by those elements only.

The elements of the set, or their description, are given inside curly brackets $\{\;\;\}$:

e.g. $\{7,8,9,10\}$ defines a set by a list and this same set is described by $\{x\in{\mathbb Z}\mid\, 7\le x\le 10\}$,

where $\mid$ means *such that*, and ${\mathbb Z}$ is the set of all integers. (Often $:$ is used instead of $\mid$ for *such that*).

We have $7\not\in S$, for $S$ given by: