- No gaps, no overlaps - Mutually exclusive, collectively exhaustive - Orthogonal - Partition >[!Aside] >My wife says that whenever I say MECE (/ˈmiːsi/, or MEE-see) she can't help but hear Jar Jar Binks. # Partition *Claude 3.5 Haiku says* I'll explain the concept of a partition in the context of set theory and how it relates to the notion of mutually exclusive and collectively exhaustive sets. In mathematics, specifically in set theory and category theory, a partition is a way of dividing a set into a collection of non-overlapping (mutually exclusive) subsets that completely cover the entire original set (collectively exhaustive). Let me break this down more precisely: - Mutually Exclusive: This means that no two subsets in the partition have any elements in common. In other words, the intersection of any two different subsets is an empty set. - Collectively Exhaustive: This means that every element of the original set is contained in at least one of the subsets. When you combine all the subsets, you get back the entire original set. A simple example might help illustrate this: Consider the set of all integers. One possible partition would be: 1. Positive integers 2. Negative integers 3. Zero These subsets are: - Mutually Exclusive: No number can be in more than one of these categories - Collectively Exhaustive: Every integer falls into exactly one of these three categories In more abstract mathematical terms, if S is your original set and {A₁, A₂, ..., Aₙ} is a collection of subsets, it's a partition if: 1. ∀i ≠ j, Aᵢ ∩ Aⱼ = ∅ (mutually exclusive) 2. ⋃ᵢAᵢ = S (collectively exhaustive)