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Every rational number has a unique representation as an irreducible fraction.
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Every and rational
Every real number, whether integer, rational, or irrational, has a unique location on the line.
Every rational soul has naturally a good free-will, formed for the choice of what is good.
Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.
Every real number, rational or not, is equated to one and only one cut of rationals.
Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.
* Every rational number has an essentially unique continued fraction representation.
* Every free abelian group is torsion-free, but the converse is not true, as is shown by the additive group of the rational numbers Q.
Every rational action must set before itself not only a principle, but also an end.
Every positive rational number can be represented by an Egyptian fraction.
Every polynomial function is a rational function with.
Every rational variety, including the projective spaces, is rationally connected, but the converse is false.
Every positive rational number can be expanded as an Egyptian fraction.
Every irreducible non-degenerate curve of degree is a rational normal curve.
Every non-singular rational surface can be obtained by repeatedly blowing up a minimal rational surface.
Every positive rational number q may be expressed as a continued fraction of the form
Every and number
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 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 dual number has the form z = a + bε with a and b uniquely determined real numbers.
# 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 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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