With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary. The boundary does not pass between ...

Adrian Moore continues his exploration of two and a half millennia of philosophical thought on infinity. Discover the brilliant but tortured German mathematician, Georg Cantor, who devised a way of ...

What largeness and structural assumptions on A ⊆ [ℝ]ω can guarantee the existence of a non-empty perfect set P ⊆ ℝ such that [P]ω ⊆ A? Such a set P is called A-homogeneous. We show that even if A is ...