Irrationality exponent of π

OpenAI published a proof that the irrationality exponent of π, μ(π), equals 2, according to the company's announcement. The result places π at the value shared by almost all real numbers, where rational numbers have μ(x) = 1 and irrational numbers satisfy μ(x) ≥ 2.

For a real number x, the irrationality index μ x is a way of measuring how well x can be approximated by rational numbers. If x is rational, μ x = 1. If x is irrational, μ x ≥ 2. OpenAI recently published a proof that μ π = 2. Almost all real numbers have irrationality exponent 2, so the new result says … The post