An isomorphism is a one to one mapping of the elements of one set onto another such that the result of an operation on the elements of one set are identical to the result of the same operation on the elements of the other set. An isomorphism is also known as bijective morphism, a mapping of one set onto another set without the loss of information. Isomorphism is derived from the two Greek words iso and morphism. The Greek word iso means equal or identical. The Greek word morphism is actually composed of two other Greek words, morph meaning form or shape and ism indicating an action. Combining these two words together into morphism yields a word meaning to form or shape. The symbol indicating isomorphic behavior is usually denoted as ( and is written A ( B, meaning A is isomorphic to B. This symbol is also sometimes used...