** Every field has an algebraic closure.

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

Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.

Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.

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

Every algebraic structure has its own notion of homomorphism, namely any function compatible with the operation ( s ) defining the structure.

* Every nonempty affine algebraic set may be written uniquely as a union of algebraic varieties ( where none of the sets in the decomposition are subsets of each other ).

Every field has an algebraic closure, and it is unique up to an isomorphism that fixes F.

* Every holomorphic vector bundle on a projective variety is induced by a unique algebraic vector bundle.

* Every ( biregular ) algebraic automorphism of a projective space is projective linear.

* Every algebraic extension of k is separable.

* Every real algebraic number field K of degree n contains a PV number of degree n. This number is a field generator.

* Every substructure is the union of its finitely generated substructures ; hence Sub ( A ) is an algebraic lattice.

Also, a kind of converse holds: Every algebraic lattice is isomorphic to Sub ( A ) for some algebra A.

* 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 finite poset is directed complete and algebraic.

* Let K < sup > a </ sup > be an algebraic closure of K containing L. Every embedding σ of L in K < sup > a </ sup > which restricts to the identity on K, satisfies σ ( L ) = L. In other words, σ is an automorphism of L over K.

Every algebraic plane curve has a degree, which can be defined, in case of an algebraically closed field, as number of intersections of the curve with a generic line.

Every planar graph has an algebraic dual, which is in general not unique ( any dual defined by a plane embedding will do ).

* 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 space filling curve hits some points multiple times, and does not have a continuous inverse.

Every point on the Lorenz curve represents a statement like " the bottom 20 % of all households have 10 % of the total income.

Every immersed curve in the plane admits two possible orientations.

Every study has found that instead of people's MBTI scores clustering around two opposite poles, such as intuition vs. sensation, with few people scoring in the middle, people's scores actually cluster around the middle of each scale in a bell curve.

Every Edwards curve with a point of order 3 can be written in the ways shown above.

Every closed curve c on X is homologous to for some simple closed curves c < sub > i </ sub >, that is,

Every minimal projective ruled surface other than the projective plane is the projective bundle of a 2-dimensional vector bundle over some curve.

Every irreducible non-degenerate curve of degree is a rational normal curve.

Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.

Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

Also among the early 32 members were syndicated panel cartoonists Dave Breger ( Mister Breger ), George Clark ( The Neighbors ), Bob Dunn ( Just the Type ) and Jimmy Hatlo ( They'll Do It Every Time ); freelance magazine cartoonists Abner Dean and Mischa Richter, editorial cartoonists Rube Goldberg ( New York Sun ), Burris Jenkins ( New York Journal American ), C. D. Batchelor ( Daily News ) and Richard Q. Yardley ( The Baltimore Sun ); sports cartoonist Lou Hanlon ; illustrator Russell Patterson and comic book artists Joe Shuster and Joe Musial.

* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.

* Every representable functor C → Set preserves limits ( but not necessarily colimits ).

Every year since 1982, the W. C. Handy Music Festival is held in the Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music and R & B.

According to Canon C. 24, " Every priest having a cure of souls shall provide that, in the absence of reasonable hindrance, Morning and Evening Prayer daily and on appointed days the Litany shall be said in the church, or one of the churches, of which he is the minister.

" Canon C. 26 stipulates that " Every clerk ( cleric ) in Holy Orders is under obligation, not being let ( prevented ) by sickness or some other urgent cause, to say daily the Morning and Evening Prayer ...." In other Anglican provinces, the Daily Office is not a canonical obligation but is strongly encouraged.

* Every cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.

Every state on a C *- algebra is of the above type.

Every fall, FRC Action ( the political action group affiliated with FRC ) holds an annual summit composed for conservative Christian activists and evangelical voters in Washington, D. C.

Every year, dozens of graduates go on to elite colleges, and T. C.

This means that A is not necessarily better than B, and B is not necessarily better than C. Every class is independent of the others.

* Every finite-dimensional simple algebra over R must be a matrix ring over R, C, or H. Every central simple algebra over R must be a matrix ring over R or H. These results follow from the Frobenius theorem.

* Every finite-dimensional simple algebra over C must be a matrix ring over C and hence every central simple algebra over C must be a matrix ring over C.