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Some Related Sentences
** and theorem
** 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
.
** The Vitali
theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable
.
** 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 Every
** Every surjective function has a right inverse
.
** Zorn's lemma
: Every non-empty partially ordered
set in which every chain ( i
. e
. totally ordered subset ) has an upper bound contains at least one maximal element
.
** Tukey's lemma
: Every non-empty collection of finite character has a maximal element with respect to inclusion
.
** Antichain principle
: Every partially ordered
set has a maximal antichain
.
** Every vector space has a basis
.
** Every unital ring other than the trivial ring contains a maximal ideal
.
** Every infinite game in which is a Borel subset of Baire space is determined
.
** Every field has an algebraic closure
.
** Every field extension has a transcendence basis
.
** Every Tychonoff space has a Stone – Čech compactification
.
** 2 ( 2012 ) (
Every hospital, airport and military base has Helipads
.
** It Happens
Every Spring-Valentine Davies, Shirley Smith
** Every voiced consonant is written with a deep letter similar in shape to the corresponding voiceless consonant which in turn is written with a tall letter
.
** The Fugitive Guy
: Every so often, Letterman would introduce " Roger Campbell " ( Elliott, wearing an extremely bad toupée ), a new member of the Late Night crew
.
** Edwin Hawkins for "
Every Man Wants To Be Free " performed by the Edwin Hawkins Singers
** The Police for "
Every Breath You Take "
** Luther Vandross and Marcus Miller for " Little Miracles ( Happen
Every Day )" performed by Luther Vandross
** L
. A
. Reid and Babyface for "
Every Little Step " performed by Bobby Brown
** 1908 Feb, in
Every Where Vol
. 21
** A Journey Through
Every Stage of Life
** 1664-The Concession and Agreement of the Lords Proprietors of the Province of New Caesarea, or New Jersey, to and With All and
Every the Adventurers and All Such as Shall Settle or Plant There
** Sting ( songwriter ) for "
Every Breath You Take " performed by The Police
** The Police for "
Every Breath You Take "
** Every item entry must
be within one level of its predecessor, such that each item must
be a sibling or child of the preceding item ( thus, no item
can be a grandchild of the preceding item ).
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