Page "Equivalence class" ¶ 14
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## Some Related Sentences

Every and element
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.
** 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.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.
: Every non-empty set A contains an element B which is disjoint from A.
Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.
Every repetition of insertion sort removes an element from the input data, inserting it into the correct position in the already-sorted list, until no input elements remain.
Every singleton is a terminal object, with the functions mapping all elements of the source sets to the single target element as morphisms.
Every simple module is cyclic, that is it is generated by one element.
Every element s, except a possible greatest element, has a unique successor ( next element ), namely the least element of the subset of all elements greater than s. Every subset which has an upper bound has a least upper bound.
Every element has a successor ( there is no largest element ).
* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.
Every time a pixel on a triangle is rendered, the corresponding texel ( or texture element ) in the texture must be found.
Every non-inner automorphism yields a non-trivial element of Out ( G ), but different non-inner automorphisms may yield the same element of Out ( G ).

Every and is
Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.
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 taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.
Every single problem touched on thus far is related to good marketing planning.
Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.
Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.
Every man in every one of these houses is a Night Rider.
Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Every infinite game in which is a Borel subset of Baire space is determined.
Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).
Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.
Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every and member
Every member of the family must have a vital place in its life.
Every member of the future protectionist cabinet then in parliament ( except Disraeli ) voted against the measure.
Every building society in the UK is a member of the Building Societies Association.
Every cleric in Holy Orders and every member of a religious order must publicly join in or privately read aloud ( i. e. using the lips as well as the eyes — it takes about two hours in this way ) the whole of the Breviary services allotted for each day.
Every two years the meeting is held in a different member state, and is chaired by that nation's respective Prime Minister or President, who becomes the Commonwealth Chairperson-in-Office.
Every member of this family does exactly what he or she wants to do.
Every member would have decision-making power in the firm and would be able to participate in establishing its overall policy objectives.
Every type that is a member of the type class defines a function that will extract the data from the string representation of the dumped data.
Every member was a multi-instrumentalist.
Every member of both gangs was always a potential killer even then.
Every member of the coalition promptly joined the Alliance, save for the United Kingdom.
Every three years, member nations that provide funds to the IDA gather together to replenish the IDA's resources.
Every finite tree structure has a member that has no superior.
Every member of the community was subject to criticism by committee or the community as a whole, during a general meeting.
Every six months member countries exchange information on deliveries of conventional arms to non Wassenaar members that fall under eight broad weapons categories: battle tanks, armored combat vehicles ( ACVs ), large-caliber artillery, military aircraft / unmanned aerial vehicles, military and attack helicopters, warships, missiles or missile systems, and small arms and light weapons.
Every member of the punk band The Ramones took the pseudonymous " Ramone " surname as part of their collective stage persona.
Every member of the bands or tribes receiving a land allotment is subject to laws of the state or territory in which they reside.
** The Fugitive Guy: Every so often, Letterman would introduce " Roger Campbell " ( Elliott, wearing an extremely bad toupée ), a new member of the Late Night crew.
Every member of the Bene Gesserit is conditioned into singular loyalty to the order and its goals with allegiances to even family being secondary, and no goal is more paramount than the Sisterhood's large-scale breeding program.
Every career member of the department is minimally licensed as an emergency medical technician, while several also hold Paramedic certification.
Every Township board and department has at least one member of Committee as a liaison.
The International Committee of the Red Cross 1958 Commentary on 1949 Geneva Convention IV Relative to the Protection of Civilian Persons in Time of War states: " Every person in enemy hands must have some status under international law: he is either a prisoner of war and, as such, covered by the Third Convention, a civilian covered by the Fourth Convention, or again, a member of the medical personnel of the armed forces who is covered by the First Convention.
Every member of the staff participated in breaking down and analyzing the stories they conceived.
Every member sings vocals, with Jughead handling the bass voice on a few tracks.

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