  Aristotle argues that in the case of magnitudes, an infinitely large magnitude and an infinitely small magnitude cannot exist. In fact, he thinks that universe is finite in size. He also agrees with Anaxagoras, that given any magnitude, it is possible to take a smaller. Hence, he allows that there are infinite magnitudes in a different sense. Since it is always possible to divide a magnitude, the series of division is unending and so is infinite. This is a potential, but never actual infinite. For each division potentially exists. Similarly, since it is always possible to add to a finite magnitude that is smaller than the whole universe continually smaller magnitudes, there is a potential infinite in addition. That series too need never end. For example, if I add to some magnitude a foot board, and then less than a half a foot, and then less than a fourth, and so forth, the total amount added will never exceed two feet. Aristotle claims that the mathematician never needs any other notion of the infinite.