Mathematicians who are finitists.

[Smaug]

Interesting. Never heard of it before.

I'd say that rejecting infinite mathematical objects is pointless. In Math everything goes as long as it satisfies certain set of pre-defined rules. Mathematical objects can be purely abstract.

There are a small group of mathematicians and a somewhat larger group of philosophers (such as William Lane Craig) who reject the fact that the set of natural numbers is an actual infinite, that is, a set of objects (albeit, "abstract") that has an infinite cardinality, that is, an infinite number of members.

But how do they deal with the "recursive arguement" (i. e. "N+1"), I wonder? Also, what about Real numbers? Not only the set itself is infinite it's also any interval from it contains infinite number of objects.