Group theory
A group is a set (collection) G whose members are called elements. The elements can be numbers of some kind, or other abstract objects. The elements can even be material objects. There is also a binary operation which combines any two elements of G and results in another element of G. This new element may be different from either of the original two, but it does not have to be: it only has to be an element of G. To be a group, the following four conditions must be true of G and the operation defined over G: