Theorem statements that involve the word ``unique'' are known as uniqueness theorems. Typically the proof of such a statement follows the idea that we assume there are two elements that satisfy the conclusion of the statement and then show that these elements are identical. As an example, consider the statement ``If the real number equation 5x+3 =a has a solution then it is unique''. A proof would look something like the following. Suppose that y and z are both solutions to the equation. Then 5y+3 =a and 5z+3 =a. Thus 5y +3 = 5z +3 from which we deduce that y = z. While this is a very simple example, the skeleton of the proof is the same for many uniqueness theorems.