# Order of a loop

From Groupprops

## Definition

The **order** of an algebra loop is defined as the cardinality of its underlying set. This generalizes the notion of order of a group, which is the special case where the loop is a group.

If the loop is a finite loop, then its order is a natural number (note that the order is at least 1 because the loop has an identity element). For an infinite loop, the order is an infinite cardinal.