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A is a subset of B, ... (also called strict) subset and proper superset respectively; that is, with the same meaning as and instead of the symbols ...
Standard set theory symbols with their usual meanings (is a member of, equals, is a subset of, is a superset of, is a proper superset of, is a proper subset of, union, intersection, empty set) ∧ ∨ → ↔ ¬ ∀ ∃ Standard logical symbols with their usual meanings (and, or, implies, is equivalent to, not, for all, there exists) ≡
The expressions "A includes x" and "A contains x" are also used to mean set membership, although some authors use them to mean instead "x is a subset of A". [2] Logician George Boolos strongly urged that "contains" be used for membership only, and "includes" for the subset relation only. [3] For the relation ∈ , the converse relation ∈ T ...
For instance, had been declared as a subset of , with the sets and not necessarily related to each other in any way, then would likely mean instead of . If it is needed then unless indicated otherwise, it should be assumed that X {\displaystyle X} denotes the universe set , which means that all sets that are used in the formula are subsets of X ...
The supremum of a subset of (,) where denotes "divides", is the lowest common multiple of the elements of . The supremum of a set S {\displaystyle S} containing subsets of some set X {\displaystyle X} is the union of the subsets when considering the partially ordered set ( P ( X ) , ⊆ ) {\displaystyle (P(X),\subseteq )} , where P ...
By the definition of subset, the empty set is a subset of any set A. That is, every element x of ∅ {\displaystyle \varnothing } belongs to A . Indeed, if it were not true that every element of ∅ {\displaystyle \varnothing } is in A , then there would be at least one element of ∅ {\displaystyle \varnothing } that is not present in A .
The Combining Diacritical Marks for Symbols block contains arrows, dots, enclosures, and overlays for modifying symbol characters. The math subset of this block is U+20D0–U+20DC, U+20E1, U+20E5–U+20E6, and U+20EB–U+20EF.
An abstract simplicial complex is a set family (consisting of finite sets) that is downward closed; that is, every subset of a set in is also in . A matroid is an abstract simplicial complex with an additional property called the augmentation property. Every filter is a family of sets.