👉 Preincreasing is a mathematical concept in set theory, which refers to a subset of a larger set that is not only strictly smaller than all its elements but also contains at least one element. It is used in the definition of a partial order. The set of all positive integers (or any natural numbers) greater than 1 is preincreasing because it does not contain any smallest or largest element, as these are included in the set itself. However, if we consider only the positive integers less
