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 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 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 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 summer form mid-June to early July, The Heart of America Shakespeare Festival has a production at Southmoreland Park near the Nelson-Atkins Museum.

Every RFC is submitted as plain ASCII text and is published in that form, but may also be available in other formats.

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 synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.

Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.

Every dual number has the form z = a + bε with a and b uniquely determined real numbers.

" Every adult had to fill out a form detailing his or her past.

Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form.

Every religion on Earth see there god in the form of light, the spread of some beam light, Islam noor, Christian rays of light it nothing but it Shiva.

Every one of these calendars has a year of 365 days, which is occasionally extended by adding an extra day to form a leap year, a method called " intercalation ", the inserted day being " intercalary ".

In Sikhism, Every soul who have taken form or born on earth is called Avtar.

Long created the Share Our Wealth program in 1934 with the motto " Every Man a King ", proposing new wealth redistribution measures in the form of a net asset tax on corporations and individuals to curb the poverty and homelessness endemic nationwide during the Great Depression.

Every acre was owned by someone, either a private individual or by government in the form of the Crown.

Every decision made by three of these " deputations " — and in each of them the lower clergy formed the majority — received ratification for the sake of form in general congregation, and if necessary led to decrees promulgated in session.

The title " Every Good Boy Deserves Favour " was borrowed, tongue-in-cheek, from a mnemonic used to remember the musical notes that form the lines of the treble clef: EGBDF.

Ongoing acrimony between the brothers, however, led to Tommy Dorsey's walking out to form his own band in 1935, just as the orchestra was having a hit with " Every Little Moment.

Every building in Regent Street is protected as a Listed Building, at least Grade II status, and together they form the Regent Street Conservation Area.

Every action has some impact in the environment, and the environment provides feedback in the form of rewards that guides the learning algorithm.

Every Wake Forest undergraduate student who lives on campus is required to sign up for some form of a meal plan in coordination with Aramark.

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

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 >.