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

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

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

* Every root of a monic polynomial whose coefficients are algebraic integers is itself an algebraic integer.

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

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

# Every adiabat asymptotically approaches both the V axis and the P axis ( just like isotherms ).

* 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 prime ideal P in a Boolean ring R is maximal: the quotient ring R / P is an integral domain and also a Boolean ring, so it is isomorphic to the field F < sub > 2 </ sub >, which shows the maximality of P. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings.

The definition of permanent agriculture as that which can be sustained indefinitely was supported by Australian P. A. Yeomans in his 1973 book Water for Every Farm.

* Universal affirmative: Every S is a P.

Jeffrey P. Dennis, author of the journal article " The Same Thing We Do Every Night: Signifying Same-Sex Desire in Television Cartoons ," argued that SpongeBob and Sandy are not romantically in love, while adding that he believed that SpongeBob and Patrick " are paired with arguably erotic intensity.

Every object would also have a read timestamp, and if a transaction T < sub > i </ sub > wanted to write to object P, and the timestamp of that transaction is earlier than the object's read timestamp ( TS ( T < sub > i </ sub >) < RTS ( P )), the transaction T < sub > i </ sub > is aborted and restarted.

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 order-preserving self-map f of a cpo ( P, ⊥) has a least fixpoint.

Every other day, starting on the third day, the player can go after an A. P. B.

" Jeffrey P. Dennis, author of " The Same Thing We Do Every Night: Signifying Same-Sex Desire in Television Cartoons ," argued that the romantic connection between Velma and Daphne Blake is " mostly wishful thinking " because Velma and Daphne " barely acknowledge each other's existence.

# Every submodule of M is a direct summand: for every submodule N of M, there is a complement P such that M = N ⊕ P.

There's One Born Every Minute ( Los Angeles, Ca, U. S. A .: Jeremy P. Tarcher, Inc, 1976.

Every major Italian town or city has a main P. d. S.

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 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 x ⊕ x

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 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 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.