Page "Class (set theory)" ¶ 1
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## Some Related Sentences

Every and set
: 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 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 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.
** 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 lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every and class
Every element of is a member of the equivalence class.
Every system must have a class designated as " root ", with one of its creation procedures designated as " root procedure ".
# Every type of state is a powerful institution of the ruling class ; the state is an instrument which one class uses to secure its rule and enforce its preferred production relations ( and its exploitation ) onto society.
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 noun belongs to a unique number class.
Every class had a taste for beer and rum.
Every unique cultivar has a unique name within its denomination class ( which is almost always the genus ).
Every year, Skull and Bones selects fifteen men ( only ) of the junior class to join the society.
Every year he exhibited work of one class or another: occasionally a public monument in the round, like those of Pasquale Paoli ( 1798 ) or Captain Montague ( 1802 ) for Westminster Abbey, of Sir William Jones for University College, Oxford ( 1797 – 1801 ), of Nelson or Howe for St Paul's Cathedral ; more often memorials for churches, with symbolic Acts of Mercy or illustrations of Scripture texts, both commonly in low relief ( 1801 ), Miss Cromwell, Chichester ( 1800 ), Mrs Knight, Milton, Cambridge ( 1802 ), and many more ; and these pious labours he would vary from time to time with a classical piece like those of his earliest predilection.
Every class can carry a primary and secondary weapon, which are organized into " kits ".
Every winter this alpine village hosts the " White Turf " horse race on the frozen Lake St. Moritz attended by the international Upper class.
This means that A is not necessarily better than B, and B is not necessarily better than C. Every class is independent of the others.
Every naval fleet consists of a variety of ships of different sizes, and no fleet has enough resources to make every vessel supreme in its class.
Every time one levels up a class division, one is given one extra attribute point until it reaches division level 50, such that a non reincarnated char has a total of 236 points, 216 points the character can invest as there is always 5 Tactics, Clout, Education and Mechanical Aptitude to start with.
Every 2 Education raises a single Technology level, which allows units to equip higher class equipments which are more efficient and / or stronger.
Every month each school is obliged to take the students for a walk ( περίπατος ), which is usually spontaneous, decided right before the first class and an educational excursion to a museum or theater etc.
Every character class is referred to as " Shaper " in-game.
Every class prepares a float which corresponds with the Homecoming theme or related theme of school spirit as assign by school administrators.
Every finite group is a subgroup of the mapping class group of a closed, orientable surface, moreover one can realize any finite group as the group of isometries of some compact Riemann surface.
Every year, over 400 events are taking place – including concerts, opera productions, class recitals and exam concerts.
Every class in Raffles Institution has its own Class Executive Committee ( CEC ).
Every class of MBBS students has assigned to itself a name denoting the year of entry.
Every member of the class participates as a sailor, soldier or minuet dancer.

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