In the new mathematics, there are only six kinds of number. Zero (0) is not one of them. Each number can be present in an amount of 1, 2, 3, 4, etc. The amount present cannot be 0 or negative. Counting starts at 1, not 0. The total amount of one kind of number present is equal to the total amount of its counterpart. If there is a total amount of x (+1 yellow) present, then there is also a total amount of x (-1 yellow) present, and if there is a total amount of y (+1 blue) present, then there is also a total amount of y (-1 blue) present and if there is a total amount of z (+0) present, then there is also a total amount of z (-0) present.

Just as the signed integers and zero can be represented as ordered pairs of two symbols, 1 or 0, so the six numbers can be represented as ordered quaternions of two symbols (1 or 0, or + or -). Each quaternion is uniquely identified by one of its four symbols, so the amount of a number present can be determined by counting how many of that symbol are present in its quaternion representation.