If you enjoy setting up ridiculous, unbeatable loops in Magic: The Gathering, check out this list of six combos from the new ...

The idea of infinity is not new, but it has evolved over time, leading to a complex hierarchy of infinite sets that mathematicians now explore. For example, the set of natural numbers (1 ...

For example, one infinity—the one most people are familiar with—is an infinite set of natural numbers: 1, 2, 3, and so on. However, there’s also an infinite set of real numbers, which ...

But if you can assign exactly one seat to each person, then both sets are exactly the same size and thus have the same cardinality. In this way, Cantor also studied the cardinality of infinite sets.

Earlier this year, they were supercharged, appearing in two new papers that uncover infinite patterns in sets of integers — progressing by leaps and bounds past Szemerédi’s now 47-year-old theorem.

The researchers detailed these new infinite sets in a paper published on the non-peer reviewed preprint server arXiv. New Scientist described exacting cardinals as being so large that they contain ...