World Colleges Information

Definition 1.1. The Cartesian product of two nonempty sets S and T is S  T = f(s; t) j s 2 S; t 2 Tg: Definition 1.2. A binary operation on a set S 6= ; is a function : SS ! S. Definition 1.3. A semigroup is a nonempty set S coupled with an associative binary operation S  S ! S denoted (s; s0) 7! ss0. Definition 1.4. A monoid is a semigroup M with a two-sided identity element eM, sometimes denoted e.