 Page "Dual number" ¶ 0
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Every and dual * Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ". Every finite-dimensional vector space is isomorphic to its dual space, but this isomorphism relies on an arbitrary choice of isomorphism ( for example, via choosing a basis and then taking the isomorphism sending this basis to the corresponding dual basis ). Every finite-dimensional normed space is reflexive, simply because in this case, the space, its dual and bidual all have the same linear dimension, hence the linear injection J from the definition is bijective, by the rank-nullity theorem. Every linear program has a dual problem with the same optimal solution, but the variables in the dual problem correspond to constraints in the primal problem and vice versa. * Every metrisable locally convex space with continuous dual carries the Mackey topology, that is, or to put it more succinctly every Mackey space carries the Mackey topology Every planar graph has an algebraic dual, which is in general not unique ( any dual defined by a plane embedding will do ).

Every and number Every real number, whether integer, rational, or irrational, has a unique location on the line. Every real number has a ( possibly infinite ) decimal representation ; i. e., it can be written as Every node has a location, which is a number between 0 and 1. The album's lead single, " She's Every Woman " peaked at number-one on the Billboard Country Chart, however its follow-up single, " The Fever " ( a cover of an Aerosmith song ) only peaked at number 23, becoming Brooks's first released Country single to not chart on the Top 10. Every rational number has a unique representation as an irreducible fraction. Every year the International Labour Conference's Committee on the Application of Standards examines a number of alleged breaches of international labour standards. Every year from 1985 through 1993, the number of attendees tripled. Every LORAN chain in the world uses a unique Group Repetition Interval, the number of which, when multiplied by ten, gives how many microseconds pass between pulses from a given station in the chain. Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space. Every ketose will have 2 < sup >( n-3 )</ sup > stereoisomers where n > 2 is the number of carbons. Every aldose will have 2 < sup >( n-2 )</ sup > stereoisomers where n > 2 is the number of carbons. The second single from the UK release was " With Every Heartbeat ", released in late July and reached number one on the UK singles chart. # Every simple path from a given node to any of its descendant leaves contains the same number of black nodes. Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where √ is called the radical sign or radix. Every positive number a has two square roots:, which is positive, and, which is negative. Every number is thought of as a decimal fraction with the initial decimal point omitted, which determines the filing order. Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set. Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8. Every third odd number is divisible by 3, which requires that no three successive odd numbers can be prime unless one of them is 3. # Every noun belongs to a unique number class. * Hardy and Littlewood listed as their Conjecture I: " Every large odd number ( n > 5 ) is the sum of a prime and the double of a prime. Every real number has an additive inverse ( i. e. an inverse with respect to addition ) given by. Every nonzero real number has a multiplicative inverse ( i. e. an inverse with respect to multiplication ) given by ( or ). Every real number, rational or not, is equated to one and only one cut of rationals.

Every and has Every soldier in the army has, somewhere, relatives who are close to starvation. Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no. Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout. Every calculation has been made independently by two workers and checked by one of the editors. Every retiring person has a different situation facing him. Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate. Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity. `` Every woman in the block has tried that ''. : Every set has a choice function. Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set. ** 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. The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF. ** 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 small category has a skeleton. * Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ). ** Every field has an algebraic closure. ** Every field extension has a transcendence basis. ** Every Tychonoff space has a Stone – Čech compactification. * Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) = Every unit of length has a corresponding unit of area, namely the area of a square with the given side length. Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice. Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.

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