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** For every non-empty set S there is a binary operation defined on S that makes it a group.

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## 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

0.557 seconds.