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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.
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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 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 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 s
The work is much more accessible than Sana ’ i ’ s for instance ; " Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature ".
Every island has one or two short airstrips where Vanair ’ s Twin Otter planes land two or three times weekly.
Pirate luminaries such as William Kidd, Henry Every, John Bowen, and Thomas Tew made Antongil Bay and Nosy Boraha ( St. Mary ’ s Island ) ( a small island 12 miles off the north-east coast of Madagascar ) their bases of operations.
The argument over the quality of Fitzgerald ’ s translation of the Rubaiyat has, according to Dougan, diverted attention from a fuller understanding of the deeply esoteric message contained in Omar ’ s actual material – " Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature ".
Every algebraic structure has its own notion of homomorphism, namely any function compatible with the operation ( s ) defining the structure.
Every year, on Father ’ s Day weekend, the downtown streets of Logan, Ohio come alive with the celebration of the washboard, as a musical instrument.
Every two weeks, the prisoners receive “ a special meal of pork broth soup and white-flour steamed buns .” Important Chinese holidays such as New Year ’ s, National Day, and the Spring Festival are celebrated with meat dumplings, a special treat in an otherwise meatless diet.
Every year since 1979, the world ’ s top blacksmiths compete in Calgary, Alberta ; performing their craft in front of thousands of spectators to educate and entertain the public with their skills and abilities.
: Amalek is still alive today .… Every time you experience a worry or doubt about how God is running the world — that ’ s Amalek launching an attack against your soul.
* Every ten years, one of Flander ’ s largest floral displays takes place on the market square ( Grote Markt ).
Every citizen who is thirty-five or older is eligible to be nominated for the presidency ; and must be nominated by either twenty or more representatives from Houses of the Oireachtas ( similar to America ’ s House of Representatives ) or four administrative counties.
In Histriomastix, Marston satirizes Jonson ’ s pride through the character Chrisoganus ; Jonson responds by satirizing Marstons's wordy style in Every Man Out of His Humour, acted by the Lord Chamberlain's Men.
Every kind of material has unique magnetic properties, even those that we do not think of as being “ magnetic .” Different materials below the ground can cause local disturbances in the Earth ’ s magnetic field that are detectable with sensitive magnetometers.
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 motion of the lock is derived from movement of the hands rather than elements beyond the operator ’ s control, such as dirt, rust, or memory.
Press reports indicate that Bartlett ’ s Political Action Committee is named Because All Responsible Taxpayers Like Every Truth Told PAC, or BARTLETT PAC for short.
Every and except
Every member of the future protectionist cabinet then in parliament ( except Disraeli ) voted against the measure.
Every action specifically intended to prevent procreation is forbidden, except in medically necessary circumstances.
Every president since Taft, except for Jimmy Carter, threw out at least one ceremonial first ball or pitch for Opening Day, the All-Star Game, or the World Series, usually with much fanfare.
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 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 album, except 1969's The Chicago Transit Authority, 1978's Hot Streets and 1995's Night and Day: Big-Band, released by Chicago Transit Authority / Chicago has been the band name followed by a Roman numeral or numbered in some other manner.
Every state except Nebraska has a bicameral legislature, meaning that the legislature consists of two separate legislative chambers or houses.
Every deity and demi-god had been invited, except Eris, the goddess of strife ( no one wanted a troublemaker at a wedding ).
Every corn-growing country decided to increase tariffs in reaction to this, except Britain and Belgium.
Every British North Atlantic route was suspended until 1856 except Cunard's Liverpool-Halifax-Boston service.
Every evening since 1928 ( except for a period during the Second World War when Ypres was occupied by Germany ), at precisely eight o ' clock, traffic around the imposing arches of the Menin Gate Memorial has been stopped while the Last Post is sounded beneath the Gate by the local fire brigade.
Every sequence in principle has a generating function of each type ( except that Lambert and Dirichlet series require indices to start at 1 rather than 0 ), but the ease with which they can be handled may differ considerably.
Every day had the name of an agricultural plant, except the 5th ( Quintidi ) and 10th day ( Decadi ) of every decade, which had the name of a domestic animal ( Quintidi ) or an agricultural tool ( Decadi ).
Every episode except one featured a live performance by a band, including Madness, Motörhead, and The Damned.
Every state, except Arkansas and Mississippi, maintains a state FEPA ( see EEOC and state FEPA directory ).
Every closed 3-manifold has a prime decomposition: this means it is the connected sum of prime three-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).
Every day had the name of an agricultural plant, except the 5th ( Quintidi ) and 10th day ( Decadi ) of every decade, which had the name of a domestic animal or an agricultural tool, respectively.
Every province in Canada except Alberta has either a Provincial Sales Tax ( PST ) or the Harmonized Sales Tax ( HST ), which is a single, blended combination of the GST and PST.