Every real number, whether integer, rational, or irrational, has a unique location on the line.

Every rational soul has naturally a good free-will, formed for the choice of what is good.

Every rational number has a unique representation as an irreducible fraction.

Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.

Every real number, rational or not, is equated to one and only one cut of rationals.

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 rational number has an essentially unique continued fraction representation.

* Every free abelian group is torsion-free, but the converse is not true, as is shown by the additive group of the rational numbers Q.

Every rational action must set before itself not only a principle, but also an end.

Every positive rational number can be represented by an Egyptian fraction.

Every polynomial function is a rational function with.

Every rational variety, including the projective spaces, is rationally connected, but the converse is false.

Every positive rational number can be expanded as an Egyptian fraction.

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

Every positive rational number q may be expressed as a continued fraction of the form

Every form is the delimitation of a surface by another one ; it possesses an inner content, the effect it produces on one who looks at it attentively.

Every aspect of the store is mapped out and attention is paid to colour, wording and even surface texture.

Every gland is formed by an ingrowth from an epithelial surface.

Every antiseptic, however good, is more or less toxic and irritating to a wounded surface ; as a result, in surgery, the antiseptic method has been replaced by aseptic method, which is preventative in nature and relies on keeping free from the invasion of bacteria rather than destroying them when present.

Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.

Every Riemann surface is the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering is holomorphically isomorphic ( one also says: " conformally equivalent ") to one of the following:

# Every Riemannian metric on a Riemann surface is Kähler, since the condition for ω to be closed is trivial in 2 ( real ) dimensions.

# Every K3 surface is Kähler ( by a theorem of Y .- T. Siu ).

Every smooth surface S has a unique affine plane tangent to it at each point.

Every now and then, the surface water sloshes back across the ocean, bringing warm water temperatures along the eastern coasts of the pacific.

Every such black body emits from its surface with a spectral radiance that Kirchhoff labeled ( for specific intensity, the traditional name for spectral radiance ).

Every 17 years, Brood X cicadas tunnel en masse to the surface of the ground, lay eggs, and then die off in several weeks.

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

Every conic surface is ruled and developable.

Every finite group is a subgroup of the mapping class group of a closed, orientable surface, moreover one can realize any finite group as the group of isometries of some compact Riemann surface.

Every vehicle function that changes direction or speed relies on friction between the tires and the road surface.

Every single object or point is dwarfed ; the valley of the Hudson is only a wrinkle in the earth's surface.

Every surface of the vaulted ceiling is occupied with preserved fishes, stuffed mammals and curious shells, with a stuffed crocodile suspended in the centre.

Every integer 2g ' 2g matrix with < sup >*</ sup > arises as the Seifert matrix of a knot with genus g Seifert surface.

Every morning before sunrise, the floor of the owners house, or where ever it may be, is cleaned with water and the muddy floor is swept well for an even surface.

Every hyperbolic Riemann surface has a non-trivial fundamental group.

According to Dale E. Dawkins, AMC's vice-president, " Every square inch of inner surface on exterior body panels is galvanized on our Spirit, Concord, and Eagle models.

Every particular finite line, surface, or solid which may possibly be the object of our thought is an idea existing only in the mind, and consequently each part of it must be perceived.

Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.

** Well-ordering theorem: Every set can be well-ordered.

Every information exchange between living organisms — i. e. transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate.

Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.

* Every regular language is context-free because it can be described by a context-free grammar.

Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.

Every real number has a ( possibly infinite ) decimal representation ; i. e., it can be written as

Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.

Every entire function can be represented as a power series that converges uniformly on compact sets.

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 positive integer n > 1 can be represented in exactly one way as a product of prime powers:

Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

Every hyperbola is congruent to the origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that is, it can be rotated so that it opens in the desired direction and can be translated ( rigidly moved in the plane ) so that it is centered at the origin.

Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.

Every species can be given a unique ( and, one hopes, stable ) name, as compared with common names that are often neither unique nor consistent from place to place and language to language.

Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.

Every morpheme can be classified as either free or bound.

Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication.

Every document window is an object with which the user can work.

Every adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and can make arrangements for the care of his / her dependants during the trip, must perform the Hajj once in a lifetime.

Every ordered field can be embedded into the surreal numbers.

* 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 preorder can be given a topology, the Alexandrov topology ; and indeed, every preorder on a set is in one-to-one correspondence with an Alexandrov topology on that set.

Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.