[permalink] [id link]
Some Related Sentences
Every and integer

*
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 real number, whether
integer, rational, or irrational, has a unique location on
the line
.
Every positive
integer n > 1
can be represented in exactly one way
as a product
of prime powers
:
: Every even
integer greater than 2 can be expressed
as the sum of two
primes.
: Every integer which
can be written as the sum of two
primes,
can also
be written as the sum of as many
primes as one wishes, until all terms are units
.
: 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 positive
integer appears exactly once somewhere on this list
.

*
Every root
of a monic polynomial whose coefficients are algebraic integers is itself an algebraic
integer.
Every memory block in this system has an order, where
the order is an
integer ranging from 0 to a specified upper limit
.

*
Every positive
integer can be written as the sum of 73 or fewer sixth powers ( see Waring's problem ).
Every positive
integer is
the sum of at most 37 fifth powers ( see Waring's problem ).
Every integer greater than 96 may
be represented
as a
sum of distinct super-prime numbers
.
Every lattice in
can be generated from a basis for
the vector space by forming all linear combinations with
integer coefficients
.

*
Every positive
integer except 1 is a PV number
.

In mathematics, an integer-valued polynomial ( also known
as a numerical polynomial ) P ( t ) is a polynomial whose value P ( n ) is an
integer for every
integer n
. Every polynomial with
integer coefficients is integer-valued, but
the converse is not true
.
Every positive
integer can be expressed
as the sum of at most 19 fourth powers ; every sufficiently large
integer can be expressed
as the sum of at most 16 fourth powers ( see Waring's problem ).

*
Every character value is a
sum of n m < sup > th </ sup > roots
of unity, where n is
the degree ( that is,
the dimension
of the associated vector space )
of the representation with character χ and m is
the order
of g
. In particular, when F is
the field
of complex numbers, every such character value is an algebraic
integer.

A finitely-generated abelian group is indecomposable if and only if it is isomorphic to Z or to a factor group
of the form for some prime number p and some positive
integer n
. Every finitely-generated abelian group is a direct
sum of ( finitely many ) indecomposable abelian groups
.
Every integer instruction could operate on either 1-byte or 2-byte integers and could access data stored in registers, stored
as part
of the instruction, stored in memory, or stored in memory and pointed to by addresses in registers
.
Every integer 2g ' 2g matrix with < sup >*</ sup > arises
as the Seifert matrix
of a knot with genus g Seifert surface
.
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 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 real number
greater than zero or every complex number except 0 has two square roots
.
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 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
.
Every and than

**
Every unital ring other
than the trivial ring contains a maximal ideal
.

*
Every topological space X is a dense subspace
of a compact space having at most one point more
than X, by
the Alexandroff one-point compactification
.
Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function,
the constant k is no longer necessarily less
than 1 ).
Every other aspect
of film making originated in a different medium
than film ( photography, art direction, writing, sound recording ), but editing is
the one process that is unique to film
.

The work is much more accessible
than Sana ’ i ’ s for instance ; "
Every line
of the Rubaiyat has more meaning
than almost anything you could read in Sufi literature ".
Every aspect
of the collage is moving and will never
be the same more
than once, which was congruent with society at
the time
.

In Anime Essentials
: Every Thing a Fan Needs to Know, Giles Poitras wrote " More humorous and less serious looking
than the characters in
the Lodoss War series,
the stars
of Slayers provide action and laughs ".
Every new emperor after him was honored by
the Senate with
the wish felicior Augusto, melior Traiano (" luckier
than Augustus and better
than Trajan ").
Every day, there are more
than one million vehicles travelling within
the city
.
Every day, doors seem to open, and every day, we interact, perhaps more
than ever before, with
the world outside
.

In
the autumn
of 1970 Jurgen Wischnewski
of the SPD declared, ‘
Every week more
than three plans for reform come up for decision in cabinet and in
the Assembly .’ ”

The Body
of Liberties adopted in 1641 by
the Massachusetts Bay colonists states, “
Every married woman shall
be free from bodily correction or stripes by her husband, unless it
be in his own defense from her assault .” In
the United States, legal decisions in Mississippi ( 1824 ) and North Carolina ( 1868 and 1874 ) make reference to — and reject — an unnamed " old doctrine " or " ancient law " by which a man was allowed to beat his wife with a stick no wider
than his thumb
.

*
Every rule
of thumb on earth in one place-A user participation reference project based on Tom Parker's 3 best-selling books and more
than 25 years
of research
.
Every material has its own characteristic resistivity — for example rubber's resistivity is far larger
than copper's
.
0.389 seconds.