Order

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**Formal Definition**

If $G$ is a group, then the **order** $|G|$ of $G$ is the number of elements in $G$.

**Informal Definition**

The **order** of a group $G$ is the cardinality of the set associated with $G$.

**Example(s)**

The **order** of $\langle \{ a, b, 42, x_2, cow^2 \} , * \rangle$ is $5$.

**Non-example(s)**

The **order** of $\{ a, b, 42, x_2, cow^2 \}$ is not defined, since **order** is only defined on groups.

**Additional Comments**

Recall from Section 0 that, for any set $S$, $|S|$ is the cardinality of S.

Thus, the cardinality of $\{ a, b, 42, x_2, cow^2 \}$ is $5$.