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Every and real
* Every real Banach algebra which is a division algebra is isomorphic to the reals, the complexes, or the quaternions.
* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
* Every commutative real unital Noetherian Banach algebra with no zero divisors is isomorphic to the real or complex numbers.
* Every commutative real unital Noetherian Banach algebra ( possibly having zero divisors ) is finite-dimensional.
Every sequence that ran off to infinity in the real line will then converge to ∞ in this compactification.
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 holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.
Every ordered field is a formally real field.
Every ordered field is a formally real field, i. e., 0 cannot be written as a sum of nonzero squares.
* Every separable metric space is isometric to a subset of the ( non-separable ) Banach space l < sup >∞</ sup > of all bounded real sequences with the supremum norm ; this is known as the Fréchet embedding.
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 dual number has the form z = a + bε with a and b uniquely determined real numbers.
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 sedenion is a real linear combination of the unit sedenions 1, < var > e </ var >< sub > 1 </ sub >, < var > e </ var >< sub > 2 </ sub >, < var > e </ var >< sub > 3 </ sub >, ..., and < var > e </ var >< sub > 15 </ sub >,
Every octonion is a real linear combination of the unit octonions:
Every real symmetric matrix is Hermitian, and therefore all its eigenvalues are real.
Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.
In his book Nirvana: The Stories Behind Every Song, Chuck Crisafulli writes that the song " stands out in the Cobain canon as a song with a very specific genesis and a very real subject ".
Every finite or bounded interval of the real numbers that contains an infinite number of points must have at least one point of accumulation.

Every and number
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 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 and greater
Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.
This was to be based on utilitarian principles ; he said: " Every man has a right to that, the exclusive possession of which being awarded to him, a greater sum of benefit or pleasure will result than could have arisen from its being otherwise appropriated.
Every element s, except a possible greatest element, has a unique successor ( next element ), namely the least element of the subset of all elements greater than s. Every subset which has an upper bound has a least upper bound.
: Every even integer greater than 2 can be expressed as the sum of two primes.
: Every integer greater than 2 can be written as the sum of three primes.
: Every integer greater than 5 can be written as the sum of three primes.
: Every even integer greater than 2 can be written as the sum of two primes,
Every aspect of the line matrix printer is designed to deliver higher reliability, fast throughput, and greater resistance to rough handling and hazardous environmental conditions.
: Every odd number greater than 7 can be expressed as the sum of three odd primes.
Every Balangay that did not gain Sanggunian Bayan status were dissolved and annexed by greater provincial or popular councils.
Every structure is associated with a certain quantity of energy, which determines the stability of the molecule or ion ( the lower energy, the greater stability ).
Boateng played a leading role in coordinating the Every Child Matters policy paper, which called for the reform of children's services, including greater accountability and coordination among government agencies.
Every year, several pieces are chosen from the greater Houston area to be produced.
Every integer greater than 96 may be represented as a sum of distinct super-prime numbers.
Every man must serve another's larger cause, giving or lending himself in whole or in part to another judgement, a further condition, a greater good, a lesser will, a common motive and purpose, and these replace his own criteria, the immediacy of his own conscience, until his own moral nature becomes a mere accessory to the cause, which is no more than his neighbour's, but the product of some ill-defined greater good and lesser evil.
Every man entered the contest intending not just to look good, but to survive, and to come away from the field worthy of greater respect.
Every number greater than 0. 3 is considered a " not kill ".
* Every individual will have a responsibility to contribute back to the greater natural and social community from his / her Brown School experience.
# Every node of level greater than one has two children.
Every state other than Vermont has a balanced budget amendment, providing some form of ban on deficits, while the Oregon kicker bans surpluses of greater than 2 % of revenue.
Every pipe or vessel is subject to heat loss when its temperature is greater than ambient temperature.
Every universe is covered by seven layers — earth, water, fire, air, sky, the total energy and false ego — each ten times greater than the previous one.

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