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.

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.

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 ...

Haddley and Worsley found that they could cut an infinite number of curved slices with an odd number of sides and even keep the delicate balance when they sliced them each in two.