- Note for the relation (specifically: partial ordering) [ilmath]\subset[/ilmath] and [ilmath]\subseteq[/ilmath] see: Subset (relation).
A subset, [ilmath]A[/ilmath], of a set [ilmath]B[/ilmath] is a set that is entirely contained in [ilmath]B[/ilmath]. That means everything contained in [ilmath]A[/ilmath] is also in [ilmath]B[/ilmath]. That is:
- [ilmath]\forall x[x\in A\implies x\in B]\iff A\subseteq B[/ilmath]