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":