The identity property is a property that obtains for addition and multiplication. In the case of addition, we write it x + 0 = x. The reason for this is obvious. If we have x, and we have nothing to it, then we are still left with x. In the case of multiplication, we write it a x 1 = a. The reason for this is that we are basically saying that a occurs one times. It should therefore come as no surprise that we are left with a. In both cases, the term applied to the variable by the relevant operation (whether addition or multiplication) produces a result that is "identical" to the initial term. Nothing is changed. The identity of the term remains. It is for this reason that the proeprty is referred to as the identity property of arithemtic.
March 20, 2014