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means that "x is an element of A". [1] Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A". 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]
In any topological space X, the empty set is open by definition, as is X. Since the complement of an open set is closed and the empty set and X are complements of each other, the empty set is also closed, making it a clopen set. Moreover, the empty set is compact by the fact that every finite set is compact. The closure of the empty set is empty.
Therefore, in this article, the Unicode version of the symbols is used (when possible) for labelling their entry, and the LaTeX version is used in their description. So, for finding how to type a symbol in LaTeX, it suffices to look at the source of the article. For most symbols, the entry name is the corresponding Unicode symbol.
The set {x: x is a prime number greater than 10} is a proper subset of {x: x is an odd number greater than 10} The set of natural numbers is a proper subset of the set of rational numbers; likewise, the set of points in a line segment is a proper subset of the set of points in a line.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
Manche Symbole sind in jedem LaTeX-2ε-System verfügbar; andere benötigen zusätzliche Schriftarten oder Pakete, die nicht notwendig in jeder Distribution mitgeliefert werden und daher selbst installiert werden müssen.
The indicator or characteristic function of a subset A of some set X maps elements of X to the codomain { , } . This mapping is surjective only when A is a non-empty proper subset of X . If A = X , {\displaystyle \ A=X\ ,} then 1 A ≡ 1 . {\displaystyle \ \mathbf {1} _{A}\equiv 1~.}
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 ...