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Powerset Axiom
In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: :\forall x \, \exists y \, \forall z \, [z \in y \iff \forall w \, (w \in z \Rightarrow w \in x)] where ''y'' is the Power set of ''x'', \mathcal(x). In English, this says: :Given any Set (mathematics), set ''x'', Existential quantification, there is a set \mathcal(x) such that, given any set ''z'', this set ''z'' is a member of \mathcal(x) if and only if every element of ''z'' is also an element of ''x''. More succinctly: ''for every set x, there is a set \mathcal(x) consisting precisely of the subsets of x.'' Note the subset relation \subseteq is not used in the formal definition as subset is not a primitive relation in formal set theory; rather, subset is defined in terms of set membership, \in. By the axiom of extensionality, the set \mathcal(x) is unique. The axiom of power set appears in mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hasse Diagram Of Powerset Of 3
Hasse is both a surname and a given name. Notable people with the name include: Surname: * Clara H. Hasse (1880–1926), American botanist * Helmut Hasse (1898–1979), German mathematician * Henry Hasse (1913–1977), US writer of science fiction * Johann Adolph Hasse Johann Adolph Hasse (baptised 25 March 1699 – 16 December 1783) was an 18th-century German composer, singer and teacher of music. Immensely popular in his time, Hasse was best known for his prolific operatic output, though he also composed a co ... (1699–1783), German composer * Maria Hasse (1921–2014), German mathematician * Peter Hasse (c. 1585–1640), German organist and composer Given name or nickname: * Hans Alfredson (born 1931), Swedish actor, film director, writer and comedian * Hans Backe (born 1952), Swedish football manager * Hasse Borg (born 1953), Swedish footballer * Hasse Börjes (born 1948), Swedish speed skater * Hasse Ekman (1915-2004), Swedish film director and actor * Hans Wind (1919†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |