Given an element $g$ of group $(G,+)$ (which henceforth we abbreviate simply as $G$), the order of $g$ is the number of times we must add $g$ to itself to obtain the identity element $e$.

Conventionally, the identity element itself has order $1$.

Examples

In the group $Z$ of integers under addition, every element except $0$ has infinite order. $0$ itself has order $1$, being the identity.