* 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 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 >.

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

Every computable relation is defined to be and.

Every peculiarity of diction, every particle, every sign, is to be considered as of higher importance, as having a wider relation and as being of deeper meaning than it seems to have.

Every constraint is in turn a pair ( usually represented as a matrix ), where is an-tuple of variables and is an-ary relation on.

Every relation can be extended in a similar way to a transitive relation.

Every day, having hardly finished working in the surgery room, Favaloro would spend hours and hours reviewing coronary angiograms and studying coronary arteries and their relation with the cardiac muscle.

Every employment relation leaves the employer with a residue of discretion, historically expressed as the ‘ master-servant ’ relationship.

Every student is continuously evaluated, corrected, and mentored, with special attention paid to the smallest of details, such as the placement of a finger within 1 / 4 inch of its required location along a trouser seam, angle of the weapon, and positioning of the student in relation to the unit.

We express this relation by means of the notation ∠( h, k ) ≅ ( h ′, k ′) Every angle is congruent to itself ; that is, ∠( h, k ) ≅ ( h, k ) or ∠( h, k ) ≅ ( k, h )

Every map consists of numerous textured polygons carefully positioned in relation to one another.

* Every relation in L ( R ) can be uniformized, but not necessarily by a function in L ( R ).

" Every legal relation " proclaims Pashukanis, " is a relation between subjects ".

" He continues: " Every category ... every description of existence or relation, is necessarily a transcript from our own nature and our own experience.

Every CSP can also be considered as a conjunctive query containment problem.

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 server uses its own query logic and structure.

Every " blob " clicked added another word to the search query.

Every search result shows a histogram traffic chart of the messages matching the query, and also the top matching lists and senders.

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.