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** For every non-empty set S there is a binary operation defined on S that makes it a group.
Some Related Sentences
** and For
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** 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 )
** and every
** 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.
** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.
** The microcode can employ both pipelines to enable auto-repeating instructions such as rep movsw perform one iteration every clock cycle, while the 80486 needed three clocks per iteration ( and the earliest x86-chips significantly more than the 486 ).
** United Kingdom Census held, the first to record names and approximate ages of every household member and to be administered nationally.
** Circuit analysis, the process of finding the voltages across, and the currents through, every component in an electrical circuit
** Unique factorization domain, an integral domain in which every non-zero element can be written as a product of irreducible elements in essentially a unique way
** Atomic domain, an integral domain in which every non-zero non-unit is a finite product of irreducible elements
** Dedekind domain, an integral domain in which every nonzero proper ideal factors into a product of prime ideals
** GCD domain, an integral domain in which every two non-zero elements have a greatest common divisor