the other, and match each element of one with its counterpart in the other. If neither falls short of the other at the opposite end, a thing with something added to it would be equal to that thing without the addition. If one falls short, it is finite; the other exceeds it by a finite amount and is therefore also finite.”

Al-Urmawī said:

“One might say that the shorter series does not terminate at its beginning. A thing with something added to it is equal to that thing without the addition only when the elements of the larger series are equal to those of the smaller, as with the sequences of numbers from one to infinity and from ten to infinity, when we align one series with the other.”

I say:

The objector has not demonstrated the invalidity of the argument, but merely offered a counterargument. Someone else might deny both premises, or one of them.

The objector says:

“If one falls short, it is finite.”

We reply: It would only be finite if it terminated