Empty Set

Various possible properties of sets are Trivially true for the empty set. NOTATION The standard notation for denoting the empty set is the symbol $arnothing$ or ∅, introduced by the and the Greek Letter Φ . Another common notation for the empty set is {}. For comparison, see the three signs together: ∅ Øø Φ – the empty set sign is based on a geometric Circle , whereas the Scandinavian letter is like an oval letter ' O '. The empty set "∅" has the unicode code point U+2205. Common TeX packages offer `\emptyset` and `arnothing`, which respectively appear as: : $\emptyset, arnothing$ PROPERTIES (Here we use Mathematical Symbol s.) For Any set ''A'', the empty set is a Subset of ''A'': : ∀''A'': ∅ ⊆ ''A'' For any set ''A'', the Union of ''A'' with the empty set is ''A'': : ∀''A'': ''A'' ∪ ∅ = ''A'' For any set ''A'', the Intersection of ''A'' with the empty set is the empty set: : ∀''A'': ''A'' ∩ ∅ = ∅ For any set ''A'', the Cartesian Product of ''A'' and the empty set is empty: : ∀''A'': ''A'' × ∅ = ∅ The only subset of the empty set is the empty set itself: : ∀''A'': ''A'' ⊆ ∅ ⇒ ''A'' = ∅ The number of elements of the empty set (that is its Cardinality ) is Zero ; in particular, the empty set is Finite :
	Any Axiom That States The Existence Of Any Set Will Imply The Axiom Of Empty Set, Using The	"http://wwwinformationdelightinfo/encyclopedia/entry/axiom_schema_of_separation" class="copylinks">Axiom Schema Of Separation For example, if ''A'' is a set then the axiom schema of separation allows the construction of the set ''B'' = {''x'' in ''A'' ''x'' &ne ''x''}, which can be defined to be the empty set

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	CATEGORIES ABOUT EMPTY SET

	basic concepts in set theory

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Empty Set