Definitions
,
Results
,
Conjectures
▾
Set of symbols
▾
Alphabet
▾
Deduction system
▾
Theory
▾
Zermelo-Fraenkel set theory
▾
Set
Subset
Formulation 0
Let $X$ be a
D11: Set
.
A
D11: Set
$E$ is a
subset
of $X$ if and only if \begin{equation} \forall \, x \in E : x \in X \end{equation}
Also known as
Combination, Unary relation
Conventions
Convention 0
(Notation for subset relation) : If $X$ is a
D11: Set
and $E$ is a
D78: Subset
of $X$, we denote this by $E \subseteq X$.
Child definitions
»
D80: Power set
»
D101: Proper subset
»
D954: Superset
Results
»
R125: Subset relation is reflexive
»
R2741: Set equality iff inclusion in both directions
»
R2745: The only subset of finite set with same cardinality is the ambient set itself
»
R108: Inclusion iff reverse inclusion of complements