Group Order
Definition 1.4 – Group Order
The order of a group, $\lvert G \rvert$, is the number of elements in the set. For instance, some group $G = \{ g_{0}, g_{1}, g_{2}, \dots, g_{n -1} \}$ has an order $\lvert G \rvert = n$.
The order of a group, and the nature of the elements, distinguishes three kinds of groups.
- Finite Group: the order is finite
- Discrete Group: the order is infinite, but the elements are countable (e.g. integers)
- Infinite Group: the order is infinite