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Some Related Sentences
Every and positive
Every positive number
a has two square roots
:, which is
positive, and, which is negative.

< li
> Every positive definite matrix is invertible and its inverse is also
positive definite.
Every positive integer appears
exactly once somewhere on this list.
Every positive real number x has
a single
positive nth root, which is written.
Every non-zero number x, real or complex, has
n different complex number nth roots including any
positive or negative roots, see complex roots below.
Every line
of a GEDCOM file begins with
a level number where all top-level records ( HEAD, TRLR, SUBN, and each INDI, FAM, OBJE, NOTE, REPO, SOUR, and SUBM ) begin with
a line with level 0, while other level numbers are
positive integers.
Every positive rational number
can be represented by an Egyptian fraction.

*
Every subset
of may
be covered by
a finite set
of positive orthants, whose apexes all belong to

*
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 positive integer except
1 is
a PV number.
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 ).

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 C *- algebra has an approximate identity
of positive elements
of norm ≤
1 ; indeed, the net
of all
positive elements
of norm ≤
1 ;
in A with its natural order always suffices.

'
Every positive law, or every law simply and strictly so called, is set, directly or circuitously, by
a sovereign person or body, to
a member or members
of the independent political society wherein that person or body is supreme.
Every positive rational number
can be expanded
as an Egyptian fraction.
Every positive integer is the sum
of at most 143 seventh
powers ( see Waring's problem ).
Every residue class
in this group contains
exactly one square free
integer, and it is common, therefore, only to consider square free
positive integers, when speaking about congruent numbers.
Every positive rational number q may
be expressed
as a continued fraction
of the form
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 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 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 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 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.

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 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.
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 n

*
Every polynomial ring R ..., x < sub
> n </ sub
> is
a commutative R-algebra.

*
Every quadratic Bézier curve is also
a cubic Bézier curve, and more generally, every degree
n Bézier curve is also
a degree m curve for any m
> n. In detail,
a degree
n curve with control points P < sub
> 0 </ sub >, …, P < sub
> n </ sub
> is equivalent ( including the parametrization ) to the degree
n +
1 curve with control points P '< sub
> 0 </ sub >, …, P '< sub
> n +
1 </ sub >, where.
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.
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.

* 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 finite tree with
n vertices, with, has at least two terminal vertices ( leaves ).
Every random vector gives rise to
a probability measure on R < sup
> n </ sup
> with the Borel algebra
as the underlying sigma-algebra.

*
Every left ideal I
in R is finitely generated, i. e. there exist elements
a < sub
> 1 </ sub >, ...,
a < sub
> n </ sub
> in I such that I = Ra < sub
> 1 </ sub
> + ... + Ra < sub
> n </ sub >.
Every smooth submanifold
of R < sup
> n </ sup
> has an induced Riemannian metric g
: the inner
product on each tangent space is the restriction
of the inner
product on R < sup
> n </ sup >.
Every finite group
of exponent
n with m generators is
a homomorphic image
of B < sub
> 0 </ sub >( m,
n ).
Every smooth manifold defined
in this
way has
a natural diffeology, for which the plots correspond to the smooth maps from open subsets
of R < sup
> n </ sup
> to the manifold.
Every known Sierpinski number k has
a small covering set,
a finite set
of primes with at least
one dividing k · 2 < sup
> n </ sup >+
1 for each
n > 0.
0.608 seconds.