Yes — Cantor named it aleph-null, written with the first Hebrew letter.
Aleph-null is the size of the whole numbers, the smallest infinite size. Anything you can pair off one-to-one with the whole numbers — like the even numbers or the fractions — also has size aleph-null. The reals between 0 and 1 are too plentiful to pair off that way, so their infinity is larger.
