Examples
Structures encountered so far
A variation
Maps
Words
(Z,+), (Z, ·), (Z/nZ,+),
(Z/nZ, ·),
(R[X],+),
(R[X], ·),
(Q[X]/(f),+),
(Q[X]/(f),·), ...
(2Z,+) and (2Z,·) are also semi-groups.
Let X be a set. The set of all maps X -> X is a semi-group
with respect to composition of maps.
Let
A be an alphabet, e.g.,
A={a,b, ..., z}.
The set of all words over the alphabet
A, that is,
all strings of letters from
A, is a semigroup with respect to
concatenation, that is, the operation that just puts the second argument behind the first.
For example, using . for the operation,
conca . tenation = concatenation