Element
Definition
An element (or member) of a set \(S\) is any object that belongs to \(S\).
We write \(x \in S\) to mean "\(x\) is an element of \(S\)."
Notation
| Symbol | Meaning |
|---|---|
| \(x \in S\) | \(x\) is an element of \(S\) |
| \(x \notin S\) | \(x\) is not an element of \(S\) |
Properties
Determinacy
For any object \(x\) and any set \(S\), exactly one of the following holds: \(x \in S\) or \(x \notin S\).
Examples
Example 1
\[2 \in \{1, 2, 3\}\]
Example 2
\[4 \notin \{1, 2, 3\}\]
Example 3
\[\emptyset \notin \emptyset\]
But \(\emptyset \in \{\emptyset\}\).
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