👉 In mathematics, "perfectiveness" refers to a property that a mathematical structure or object possesses such that its properties are consistent with the axioms of the theory. In other words, it is an attribute that is true for all objects in the theory and that can be proven without contradiction. For example, consider a set X of natural numbers. We might define "perfectness" as follows: a subset A of X is perfect if every element of A is a member of X, i.e.,