Closure Operation

3.     m-operator.

Let g(x₁, ..., x_n, y) be a function such that for all x₁, ..., x_n there is y such that

g(x₁, ..., x_n, y) = 0. Then, by definition,

my(g(x₁, ..., x_n, y) = 0) is the least y such that g(x₁, ..., x_n, y) = 0.

        Here m is called the least number operator. For such a function g, the function f where

f(x₁, ..., x_n, y) = my(g(x₁, …, x_n,y) = 0)

        is said to be obtained from g by the m-operator.