Order

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Formal Definition

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

Informal Definition

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

Example(s)

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

Non-example(s)

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

Additional Comments

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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 $5$.