Let a 1 , a, ... be a sequence of elements in a semigroup G. Then there exists a unique function : N*

Let a₁, a, ... be a sequence of elements in a semigroup G. Then there exists a unique function ψ : N* → G such that ψ(1) = a₁, ψ(2) = a₁a₂, ψ(3) = (a₁a₂)a₃ and for n ≥ 1,ψ(n + 1) = (ψ(n))a_n+1- Note that ψ(n) is precisely the standard n product

72 II i=1 ai.