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Page "Axiom of choice" ¶ 84
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** and Vitali
** Vitali Sevastyanov

** and theorem
** Well-ordering theorem: Every set can be well-ordered.
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.
** Tychonoff's theorem stating that every product of compact topological spaces is compact.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
** Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.
** The Nielsen – Schreier theorem, that every subgroup of a free group is free.
** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals
** The theorem that every Hilbert space has an orthonormal basis.
** The Banach – Alaoglu theorem about compactness of sets of functionals.
** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.
** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.
** Hilbert's basis theorem
** Bayes ' theorem
** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.
** Lyapunov's central limit theorem
** Superposition theorem, in electronics
** " Kelvin's vorticity theorem for incompressible or barotropic flow ".
** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem
** Various proofs of the four colour theorem.

** and on
** Eunectes murinus, the green anaconda, the largest species, is found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and on the island of Trinidad.
** For every non-empty set S there is a binary operation defined on S that makes it a group.
** See also Salmond on " Citizenship and Allegiance ," in the Law Quarterly Review ( July 1901, January 1902 ).
** This is, on the whole, an informed and good account of the life and accomplishments of one of the greatest influences on the development of thought both Eastern and Western.
** This is a distinguished work which stands out from, and above, many of the books and articles which have ben written in this century on Avicenna ( Ibn Sīnā ) ( A. D. 980 – 1037 ).
** Earliest day on which Caribana celebration can fall, celebrated on the first Weekend of August.
** Earliest day on which Emancipation Day can fall, celebrated on the first Monday of August.
** Lughnasadh, traditionally begins on the eve of August 1.
** Cadius Rufus was executed on the charge of extortion.
** Various articles on Alcidamas ( 1856 – 1919, with links to further online material )
** Gordon-Reed, Annette speaking on CSPAN Booktv Andrew Johnson
** Khmer New Year, or Chol Chnam Thmey, most commonly celebrated on April 13 ( Cambodia )
** To use a long dash on Wikipedia, type in "".
** called a god on Malta ( 28: 6 )
** Ability to run on an IA-64 architecture processor, although this never went beyond beta
** Minimum level required for POWER4 hardware and the last release that worked on the Micro Channel architecture
** Ability to run in a Logical Partition on POWER4
** Ability to run on 64-bit architecture CPUs
** Run on RS / 6000 systems with PowerPC processors and PCI busses.
** Optional POKEY sound chip on cartridge for improved sounds.
** Headphone port ( stereo ; wired for mono on the original Lynx )

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