Are All Infinities the Same Size?

There are actually many different sizes or levels of infinity; some infinite sets are vastly larger than other infinite sets. The theory of infinite sets was developed in the late nineteenth century by the brilliant mathematician Georg Cantor

Can infinities be bigger than others?

Yes. If you're given an infinite set, there is a simple method to make a larger infinity: take its power set, which is always of higher cardinality. So not only some infinities are larger than others, but there is no a "largest" inifinity, you can always create a larger one.

Are all countable infinities the same size?

The set of natural numbers is infinite. ... Because of this, Cantor concluded that all three sets are the same size. Mathematicians call sets of this size “countable,” because you can assign one counting number to each element in each set.