limit could be short of one is all but self-evidently false. Indeed, one might say that what is infinite cannot be neither even nor odd, because even and odd are the two species of the genus of bounded number, which has two endpoints: a beginning and an end.

If, however, something is supposed to have neither a beginning nor an end, it is not a bounded number and is therefore neither even nor odd. This is what Muslims and adherents of other religions say concerning the delights of Paradise that Allah Most High will bring into being in the future: they are neither even nor odd.

This is also the position of the natural philosophers and metaphysicians: what is infinite is neither even nor odd, because it has no two endpoints. An even number is one that admits division into two equal parts, and this is conceivable only where there are two finite endpoints. If something cannot be even, it cannot be odd either.

As for numerical orders, those conceived in the mind are bounded and finite. What is infinite cannot be conceived by minds; rather, however many times the mind doubles numerical orders, the result remains finite. The ranks themselves are finite, but one of the two ranks would, if its individual members existed in external reality, have more members than the first. This is not a disparity between existing things, whether in minds or in external reality.

[Third]

Abū al-Hasan al-Āmidī said:

“The third argument: If infinitely many numbers existed, each one would be bounded by existence, and so the totality would be bounded by existence. Yet what is infinite cannot be bounded by anything.”