A set $S$ plus any number of functions $f_{i}:S×S→S$, such that each $f_{i}$ satisfies some properties of choice.

Some specific examples:

The order of a algebraic structure is just its cardinality.

The degree of some algebraic structure is some parameter that describes the structure. There is no universal definition valid for all structures, it is a per structure type thing.

This is particularly useful when talking about structures with an infinite number of elements, but it is sometimes also used for finite structures.

Examples:

- the dihedral group of degree n acts on n elements, and has order 2n
- the parameter $n$ that characterizes the size of the general linear group $GL(n)$ is called the degree of that group, i.e. the dimension of the underlying matrices

Examples: