  The notions of potential infinity (understood as expressing a direction) and
actual infinity (expressing a quantity) are investigated. It is shown that the
notion of actual infinity is inconsistent, because the set of all (finite)
natural numbers which it is ascribed to, cannot contain an actually infinite
number of elements. Further the basic inequality of transfinite set theory
aleph0 < 2^aleph0 is found invalid, and, consequently, the set of real numbers
is proven denumerable by enumerating it.
