Mathematicians have long known that there are many kinds of infinities (technically, there are an infinity of them). Mathematicians revealed two new kinds of infinity—called exacting and ...

For example, the set of natural numbers (1 ... more groundbreaking revelations in the world of mathematics, reshaping our understanding of the infinite in ways we never thought possible.

However, there’s also an infinite set of real numbers ... comparing these new infinities with a foundational concept of mathematics known as the Axiom of Choice, which says that you can make ...

The researchers detailed these new infinite sets in ... a foundational concept of mathematics known as the Axiom of Choice, which says that you can make a new set of numbers by picking out numbers ...