Every operation within the spacecraft that required knowledge of direction was carried out with respect to the orientation of the guidance platform, itself aligned according to a particular REFSMMAT.

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 >.

Every play is subject to booth review with coaches only having one challenge.

The album's lead single, " She's Every Woman " peaked at number-one on the Billboard Country Chart, however its follow-up single, " The Fever " ( a cover of an Aerosmith song ) only peaked at number 23, becoming Brooks's first released Country single to not chart on the Top 10.

Every Mac made between 1986 and 1998 has a SCSI port on the back, making external expansion easy ; also, " toaster " Compact Macs did not have easily accessible hard drive bays ( or, in the case of the Mac Plus, any hard drive bay at all ), so on those models, external SCSI disks were the only reasonable option.

* Every thing that was within the general rule and was excluded from the rule to teach us a rule, we don't consider this rule as pertaining only to this excluded case, but to the entire general case.

When coming to Kubla Khan, he pointed out: " instead of being content to have written finely under the influence of laudanum, recommends ' Kubla-Khan ' to his readers, not as a poem, but as ' a psychological curiosity ' ... Every lover of books, scholar or not, who knows what it is to have his quarto open against a loaf at his tea ... ought to be in possession of Mr. Coleridge's poems, if it is only for ' Christabel ', ' Kubla Khan ', and the ' Ancient Mariner '.

Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.

Every reduction step acts only on the rightmost, newest parse fragments.

Every one thinks chiefly of his own, hardly at all of the common interest ; and only when he is himself concerned as an individual.

Every legion had a large baggage train which included 640 mules ( 1 mule for every 8 legionaries ) only for the soldiers ' equipment.

Every quark in the universe does not attract every other quark in the above distance independent manner, since colour-confinement implies that the strong force acts without distance-diminishment only between pairs of single quarks, and that in collections of bound quarks ( i. e., hadrons ), the net colour-charge of the quarks cancels out, as seen from far away.

Eastwood's only comedies have been Every Which Way but Loose ( 1978 ) and its sequel Any Which Way You Can ( 1980 ), which are his two most commercially successful films after adjustment for inflation.

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

Every tree with only countably many vertices is a planar graph.

* Every connected graph with only countably many vertices admits a normal spanning tree.

Every new Lodge must be warranted or chartered by a Grand Lodge, but is subject to its direction only in enforcing the published Constitution of the jurisdiction.

" In an interesting meditation on what he viewed as the harm which would result if Christian ideals were abandoned in Belgium, he said: " Every time society has distanced itself from the Gospel, which preached humility, fraternity, and peace, the people have been unhappy, because the pagan civilization of ancient Rome, which they wanted to replace it with, is based only on pride and the abuse of force " ( Commemorative speech for the war dead of the Battle of the Yser, given by Dom Marie-Albert, Abbot of Orval Abbey, Belgium, in 1936 ).

# Every satisfiable set of formulas is consistent, where a set of formulas is satisfiable if and only if there exists a model such that.

Other sauces are either prepared from scratch, or are variations on a basic curry sauce :< ref ><" Every restaurant has a large pan of this sauce always at hand, with the recipe varying only slightly from Chef to Chef.

Every type of terminal had a hard-wired communications card which supported only the operation of one type of terminal without compatibility with other types of terminals on the same line.

The directive declared, " Every military commander has the responsibility to oppose discriminatory practices affecting his men and their dependents and to foster equal opportunity for them, not only in areas under his immediate control, but also in nearby communities where they may live or gather in off-duty hours.

Pope John Paul II explained in his Apostolic Letter Salvifici Doloris ( 11 February 1984 ):" In the Cross of Christ not only is the Redemption accomplished through suffering, but also human suffering itself has been redeemed ... Every man has his own share in the Redemption.

Every fourth Coptic year is a leap year without exception, as in the Julian calendar, so the above mentioned new year dates apply only between 1900 and 2099 inclusive in the Gregorian Calendar.

The album and its two singles " Every Shade of Blue " and " Take Me to Your Heart " were only released in some European countries, North America, Japan and Australia, and not in Britain.

Every craft produces its own marks, and the supply is kept constant, new marks only being produced to replace old ones.