Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

Every system must have a class designated as " root ", with one of its creation procedures designated as " root procedure ".

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 nth root of unity z is a primitive ath root of unity for some a where 1 ≤ a ≤ n: if z < sup > 1 </ sup >

Every word must have only one root ( free morpheme ) always at the beginning.

Every positive real number x has a single positive nth root, which is written.

Every real polynomial of odd degree has at least one real number as a root.

Every name lookup must either start with a query to a root server or use information that was once obtained from a root server.

Every element of the Quran is mathematically composed — the suras, the verses, the words, the number of certain letters, the number of words from the same root, the number and variety of divine names, the unique spelling of certain words, the absence or deliberate alteration of certain letters within certain words, and many other elements of the Quran besides its content.

Every pipe is placed in the root directory of the named pipe filesystem ( NPFS ), mounted under the special path ( that is, a pipe named " foo " would have a full path name of

; Sherrington's First Law: Every posterior spinal nerve root supplies a particular area of the skin, with a certain overlap of adjacent dermatomes.

* Every irreducible polynomial in K which has a root in L factors into linear factors in L.

Every prime power ( except powers of 2 ) has a primitive root ; thus the multiplicative group of integers modulo p < sup > n </ sup > ( or equivalently, the unit group of the ring ) is cyclic.

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

Every polynomial P in x corresponds to a function, ƒ ( x )

Every output of an encoder can be described by its own transfer function, which is closely related to the generator polynomial.

Every polynomial in can be factorized into polynomials that are irreducible over F. This factorization is unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over a field is a unique factorization domain whose units are the nonzero constant polynomials ).

Every delta operator ' has a unique sequence of " basic polynomials ", a polynomial sequence defined by three conditions:

* Every irreducible closed subset of P < sup > n </ sup >( k ) of codimension one is a hypersurface ; i. e., the zero set of some homogeneous polynomial.

* Every Jacobi-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

* Every Laguerre-like polynomial sequence can have its domain shifted, scaled, and / or reflected so that its interval of orthogonality is, and has Q =

* Every Hermite-like polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality is, and has Q

Every polynomial function is a rational function with.

* Every irreducible polynomial over k has distinct roots.

* Every polynomial over k is separable.

Every field and every polynomial ring over a field ( in arbitrarily many variables ) is a reduced ring.

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 library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

# Every sequence in A has a convergent subsequence, whose limit lies in A.

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations.

Every cycle climaxes in the arrival of The Leveler, whose approach ( and fall ) is heralded by an ominous comet that appears in the sky.

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 congruence relation has a corresponding quotient structure, whose elements are the equivalence classes ( or congruence classes ) for the relation.

* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

Every morphism in a concrete category whose underlying function is injective is a monomorphism ; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily be a monomorphism in the categorical sense.

Every morphism in a concrete category whose underlying function is surjective is an epimorphism.

Every family head in the Mafia selects a man whose characteristics already make him look approachable.

She was raised there by her mother, Ellen Simmons, whose Sioux name was Taté Iyòhiwin ( Every Wind or Reaches for the Wind ).

* Every Parliament constituted in conformity with the laws of a sovereign State whose population it represents and on whose territory it functions may request affiliation to the Inter-Parliamentary Union.

" A man's home is his castle " is translated in Gor as, " Every man is an Ubar within the circle of his sword " ( The Ubar is a war-leader, a General who takes power at a time of crisis, and whose rule is tantamount to tyrant until the crisis is resolved.

* Every planar graph whose faces all have even length is bipartite.

During this period he lived with the French poet Pierre Martory, whose books Every Question but One ( 1990 ), The Landscape Is behind the door ( 1994 ) and The Landscapist he has translated ( 2008 ), as he has Jean Perrault ( Camouflage ), Max Jacob ( The Dice Cup ), Pierre Reverdy and Raymond Roussel.

Every governor since Ronald Reagan in 1968 has been subject to a recall effort, but Gray Davis was the first governor whose opponents gathered the necessary signatures to qualify for a special election.

Every artist she showed the script to had declined to take on the project, so it was offered to aspiring artist Arthur Adams, whose samples had been given to editor Carl Potts and Nocenti, his assistant editor, by editor Al Milgrom.

* Every integrable subbundle of the tangent bundle — that is, one whose sections are closed under the Lie bracket — also defines a Lie algebroid.

* Every constant function whose domain and codomain are the same is idempotent.

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