Definition:Order of Structure

Definition
The order of an algebraic structure $\struct {S, \circ}$ is the cardinality of its underlying set, and is denoted $\order S$.

Thus, for a finite set $S$, the order of $\struct {S, \circ}$ is the number of elements in $S$.

Also defined as
Some sources do not define the order of a structure for an underlying set of infinite cardinality, restricting themselves to the finite case.

Notation
Some sources use $\map o S$ for the order of $S$, but this has problems of ambiguity with other uses of $\map o n$. (See little-o notation.)

Also see
This definition is mostly used in the context of group theory:


 * Definition:Finite Group
 * Definition:Infinite Group