[permalink] [id link]
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
Some Related Sentences
** and Tarski's
** and theorem
** 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
** and For
** For example, consider the map ( which is the " realification " of the complex square function ) where U
** For some verbs in some languages, the difference between perfective and imperfective conveys an additional meaning difference ; in such cases, the two aspects are typically translated using separate verbs in English.
** For ohm – SI unit of electrical resistance ; formerly also used upside down () to represent mho, the old name for the inverse of an ohm ( now siemens with symbol S ) used for electrical conductance.
** For instance, when a magazine claims that An MIT professor predicts that the robotic era is coming in 2050, the use of big-name " MIT " ( a world-renowned American university for the advanced research in math, science, and technology ) establishes the " strong " credibility.
** For example: One specific person may be identified by all of the following identifiers: Jane Smith ; Jane Elizabeth Meredith Smith ; Jane E. M. Smith ; Jane E. Smith ; Janie Smith ; Janie ; Little Janie ( as opposed to her mother or sister or cousin, Big Janie ); Aunt Jane ; Auntie Janie ; Mom ; Grandmom ; Nana ; Kelly's mother ; Billy's grandmother ; Ms. Smith ; Dr. Smith ; Jane E. Smith, PhD ; and Fuzzy ( her jocular nickname at work ).
** Existence of additive inverse: For any integer a, there exists an integer denoted by − a such that a + (− a )