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Page "Nth root" ¶ 20
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Every and non-zero
Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.
Every non-zero characteristic is a prime number.
* Every column of contains at most two non-zero entries ;
( 3 ) Every unitary representation of G that has an ( ε, K )- invariant unit vector for any ε > 0 and any compact subset K, has a non-zero invariant vector.

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 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 real number, rational or not, is equated to one and only one cut of rationals.

Every and x
* Every polynomial ring R ..., x < sub > n </ sub > is a commutative R-algebra.
Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.
* Every pair of congruence relations for an unknown integer x, of the form x ≡ k ( mod a ) and x ≡ l ( mod b ), has a solution, as stated by the Chinese remainder theorem ; in fact the solutions are described by a single congruence relation modulo ab.
Every polynomial P in x corresponds to a function, ƒ ( x )
* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.
Every Boolean ring R satisfies xx
Every finitely generated ideal of a Boolean ring is principal ( indeed, ( x, y )=( x + y + xy )).
Every positive real number x has a single positive nth root, which is written.
Every such line meets the sphere of radius one centered in the origin exactly twice, say in P = ( x, y, z ) and its antipodal point (− x, − y, − z ).
Every locally constant function from the real numbers R to R is constant by the connectedness of R. But the function f from the rationals Q to R, defined by f ( x ) = 0 for x < π, and f ( x ) = 1 for x > π, is locally constant ( here we use the fact that π is irrational and that therefore the two sets
Every empty function is constant, vacuously, since there are no x and y in A for which f ( x ) and f ( y ) are different when A is the empty set.
Every real x satisfies the inequality
Every real number x is surrounded by an infinitesimal " cloud " of hyperreal numbers infinitely close to it.

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