Originally Posted by

**Heinsbergrelatz**
is this something to do with Georg Cantor's set theory??

In fact it nothing much to do with anything, really.

What the OPer seems to be groping toward (but failing in spectacularly) is the following: Yes there (at least) two kinds of infinity as far this term refers to the

*cardinality of sets*.

However, the following might be worth pointing out: if I say there are infinitely many numbers (natural, real or complex), I actually mean the sets

are of infinite cardinality. This slight linguist abuse rarely confuses. However, the expression "x is an infinite (or finite) number" always does, and in fact makes little sense unless it refers to the cardinality of a set.

Cantor showed that, whereas a set that can be put into one-to-one correspondence with a subset of the natural (i.e. counting) numbers is

*by definition* countable (not due to him, I believe), even though it may be infinite (hence the term "countably infinite"), the set of real numbers cannot be put in such a correspondence with the set of counting numbers, and is thereby said to be "uncountably infinite".

Unfortunately, all this seems to have been too much trouble for the OPer to check up on before posting.