The size of certain infinite sets has been a mystery. Now, it turns out, each one is different than the next, and they can all be ordered by size ...

Was it true? Amid fears that set theory contained an actual contradiction — a proof of 0 = 1, which would invalidate the whole construct — math faced an existential crisis. The question, as Simpson ...

A set of the six sides of a die matches up one-to-one with a set of red shoes, helping illustrate Georg Cantor's set theorem. Image courtesy of GBH/NOVA It can be easy to take math for granted ...

This result means that the infinite apparatus in RT 2 2 can be wielded to prove new facts in finitistic mathematics, forming a surprising bridge between the finite and the infinite.

However, there’s also an infinite set of real numbers, which includes negatives and decimals. Keep following this train of thought, and you create an infinite set of infinities.

The set of real numbers, in turn, is smaller than even larger infinities, and so on. To measure the size of infinite sets, Cantor introduced so-called transfinite numbers.