: 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.

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

** 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.

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

* 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 non-empty set A contains an element B which is disjoint from A.

* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.

Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.

* Every cofinal subset of a partially ordered set must contain all maximal elements of that set.

Every corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.

Every DNS zone must be assigned a set of authoritative name servers that are installed in NS records in the parent zone, and should be installed ( to be authoritative records ) as self-referential NS records on the authoritative name servers.

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.

# " Personality " Argument: this argument is based on a quote from Hegel: " Every man has the right to turn his will upon a thing or make the thing an object of his will, that is to say, to set aside the mere thing and recreate it as his own ".

Every atom across this plane has an individual set of emission cones .</ p > < p > Drawing the billions of overlapping cones is impossible, so this is a simplified diagram showing the extents of all the emission cones combined.

* Every singleton set

Every processor or processor family has its own machine code instruction set.

Every set is a class, no matter which foundation is chosen.

Every non-empty totally ordered set is directed.

* 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 state governor since Denver S. Dickerson has resided in the Governor's Mansion located in Carson City.

" More immediately, though, he called for a massive build-up of U. S. arms production: " Every realist knows that the democratic way of life is at this moment being ' directly assailed in every part of the world … The need of the moment is that our actions and our policy should be devoted primarily — almost exclusively — to meeting this foreign peril.

Every U. S. jurisdiction has its own regulations regarding what, precisely, must be said to a person arrested or placed in a custodial situation.

Good Trouble ( 1982 ) and Wheels Are Turnin ' ( 1984 ) were follow-up albums which also did well commercially, the former containing the hit singles " Keep the Fire Burnin '" ( U. S. # 7 ), " Sweet Time " ( U. S. # 26 ) and the un-ranked " The Key " and the latter containing the # 1 hit single " Can't Fight This Feeling " plus three more hits: " I Do ' Wanna Know " ( U. S. # 29 ), " One Lonely Night " ( U. S. # 19 ), " Live Every Moment " ( U. S. # 34 ) and the un-ranked " Break His Spell ".

Every S / 360 ( except for the Model 20, which was not a standard S / 360 ) had a byte-multiplexer channel and 1 or more selector channels.

Every year, the American Chemistry Council tabulates the U. S. production volume of the top 100 basic chemicals.

The film was written by Cyril Hume ( dialogue ), John Thomas Neville, Richard Schayer and Dale Van Every and Ethelreda Lewis, and directed by W. S.

Every state highway, even those forming parts of U. S. Routes, was assigned a number.

Every February, A. Y. S. O.

Every year the community hosts the Welcome Easter Parade along the main road, Old U. S. Highway 52.

* Universal affirmative: Every S is a P.

For their next two albums, Every Good Boy Deserves Favour ( 1971 ) – from which Hayward's " The Story in Your Eyes " was taken as a US Charting single ( No. 23 ), and Seventh Sojourn ( 1972 ) ( which reached No. 1 in the U. S .), the band returned to their signature orchestral sound which, while difficult to reproduce in concert, had become their trademark.

Every summer a cherry festival is held at Lofthus, where the Norwegian championship of cherry stone spitting is held ( record: 14. 24 meters, S. Kleivkaas ).

" Every Morning ", which received widespread comparisons to " Fly ", rose to similar success during the spring of 1999, reaching No. 3 in the U. S. Billboard Hot 100 chart.

In 1991, she launched Every Child By Two, a nationwide campaign that sought to increase early childhood immunizations along with Betty Bumpers, wife of former U. S. Senator Dale Bumpers of Arkansas.

# Every candidate inside the set S is pairwise unbeaten by every candidate outside S ; and

Veneman is also co-chair of Mothers Day Every Day, along with former U. S. President Bill Clinton ’ s Health and Human Services Secretary Donna Shalala.

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.

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.