The colorable, divisible infinite sets in RT 2 2 are abstractions that have no analogue in the real world. And yet, Yokoyama and Patey’s proof shows that mathematicians are free to use this ...

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.