* 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 dilation of a Euclidean space that is not a congruence has a unique fixed point that is called the center of dilation.

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 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 the query can be accessed via a sequential scan.

* 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 soldier in the army has, somewhere, relatives who are close to starvation.

Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every calculation has been made independently by two workers and checked by one of the editors.

Every retiring person has a different situation facing him.

Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

`` Every woman in the block has tried that ''.

: Every set has a choice function.

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.

** Every surjective function has a right inverse.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.

** Antichain principle: Every partially ordered set has a maximal antichain.

** Every vector space has a basis.

* Every small category has a skeleton.

* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).

** Every field has an algebraic closure.

** Every field extension has a transcendence basis.

** Every Tychonoff space has a Stone – Čech compactification.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.

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 ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.