[IngoBlechschmid]

I totally agree that mainstream mathematics doesn't have any problem whatsoever with infinite constructions and in fact embraces them.

I just wanted to clarify that intuitionistic and constructive mathematics don't have any problems with infinite constructions either. Finitism and ultrafinitism do, but they're not what's usually called "constructive mathematics".

There are at least three orthogonal axes which you can classify mathematical schools of thought in:

* Is the law of excluded middle accepted? ("Any statement is either true or not true.")

* Are infinite sets accepted? (They are not in finitism, but they are in constructive mathematics and of course in ordinary mathematics.)

* Can constructions implicitly refer to the result of what is being constructed? Is the powerclass of a set again a set? (Yes in ordinary mathematics and in constructive mathematics, no in predicative mathematics.)