User blog comment:P進大好きbot/A Generic System Analogous to Kleene's O/@comment-37233444-20191111033045

"I denote by \(X\) the set of partial maps \(\mathbb{N} \to \mathbb{N}\)."

you mean all the different ways one finite set of natural numbers can be mapped to another finite set, such that there is a mapping for every element in both sets?

i want to make sure i get this.