## Groups

A group in terms of math is a set of numbers along with a "binary operation" (in this case called a group operation) that has the properties of closure, associativity, identity and inverse. The "binary operation" is any sort of modification to the elements. Examples of these would be the typical operands used in traditional math (+, *). If we were to have group G with elements A, B, C,... and a group operation of addition, then the properties would be applied as follows:

Closure: Since A and B are in G and the group operation is "+", the sum of A+B must be contained within the group.

Associative: (A + B) + C = A + (B + C)

Identity: A + 0 = A

Inverse: There should be some element that equals $ A^{-1} $, for example, $ A^{-1} = D $.