0. Set of symbols
1. Alphabet
2. Deduction system
3. Theory
4. Zermelo-Fraenkel set theory
5. Set
6. Subset
7. Power set
8. Hyperpower set sequence
9. Hyperpower set
10. Hypersubset
11. Subset algebra
Set partition
Formulation 0
Let $X$ be a D11: Set.
A D11: Set $\mathcal{S} \subseteq \mathcal{P}(X)$ is a set partition of $X$ if and only if
(1) \begin{equation} X = \cup \mathcal{S} \end{equation} D4984: Tight set cover
(2) \begin{equation} \forall \, E, F \in \mathcal{S} \left( E \neq F \quad \implies \quad E \cap F = \emptyset \right) \end{equation} D1681: Disjoint set collection
Child definitions
» D5150: Complement set partition
» D83: Proper set partition