👉 In mathematics, a frother is a binary relation on the set of all natural numbers that satisfies some additional properties. A frother on a set S is a relation R from S to itself such that for any a, b in S, and n in N, we have: R(a, b) = R(b, a) The frother property states that if a binary relation R exists on an arbitrary set of natural numbers S, then it must satisfy the following two properties: 1.