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 ...

Examples of infinite sets abound in mathematics. You know, we see them every day. So do those infinities exist? Think you'll get a different answer from every person, every mathematician you meet.

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.

Ever since Gödel and Cohen established the independence of the continuum hypothesis from ZFC, infinite math has been a choose-your-own-adventure story in which set theorists can force the number of ...

Defining Infinity Season 2 Episode 17 | 10m 31s | CC Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity? 08/29/2018 From ...

On the other hand, we prove an infinite dimensional analogue of Mycielski's Theorem: if A is large in the sense of a suitable Baire category-like notion, then there exists a non-empty perfect ...

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.

This monthly journal, begun in 1950, is devoted entirely to research in pure and applied mathematics, principally to the publication of original papers of moderate length. A section called Shorter ...