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** Well-ordering theorem: Every set can be well-ordered.
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.
** 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.
** 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.
** 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.
** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem
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** 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.
** 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.
** Luther Vandross and Marcus Miller for " Little Miracles ( Happen Every Day )" performed by Luther Vandross
** 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
** 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 ).