Category:Subsets

From ProofWiki
Jump to navigation Jump to search

This category contains results about Subsets.
Definitions specific to this category can be found in Definitions/Subsets.


Let $S$ and $T$ be sets.

$S$ is a subset of a set $T$ if and only if all of the elements of $S$ are also elements of $T$.

This is denoted:

$S \subseteq T$


That is:

$S \subseteq T \iff \forall x: \paren {x \in S \implies x \in T}$


If the elements of $S$ are not all also elements of $T$, then $S$ is not a subset of $T$:

$S \nsubseteq T$ means $\neg \paren {S \subseteq T}$

Pages in category "Subsets"

The following 99 pages are in this category, out of 99 total.