Infinity is the creator of great paradoxes.

Infinity is a concept of convenience. It indicates that some process goes on without limit. It is an open question whether or not infinity actually exists. Most mathematicians concede that infinity actually exists as it is incredibly convenient and useful. A few do not. Some take it to be more incomplete rather than completed.

Georg Cantor believed that infinity was a complete, nameable thing, the first of which he called "little-omega." He used the process of naming "little-omega" to name "two-little-omega" and "three-little-omega" etc. up to "little epsilon" and onward up to "Aleph-one." "Aleph-naught" turned out to be the "number" of integers, while "Aleph-One" turned out to be the "number" of real numbers.

He postulated that there were levels of infinity between "Aleph-naught" and "Aleph-one" This is called the "Continuum Hypothesis."

It might be added that his "proof" that the real numbers numbered "Aleph-one" (uncountable) relies upon The Diagonalization Proof