Every positive rational number appears exactly once in this infinite binary tree. The root is 1/1; each node p/q has left child p/(p+q) and right child (p+q)/q. Reading nodes breadth-first enumerates all rationals — a bijection ℕ → ℚ⁺.
The Stern-Brocot tree has the same nodes but different structure — every node lies between its ancestors. The Calkin-Wilf sequence a(n) satisfies a(2n)=a(n) and a(2n+1)=a(n)+a(n+1) with a(1)=1.