** 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.

Every LORAN chain in the world uses a unique Group Repetition Interval, the number of which, when multiplied by ten, gives how many microseconds pass between pulses from a given station in the chain.

# Every finitely generated ideal of A is principal ( i. e., A is a Bézout domain ) and A satisfies the ascending chain condition on principal ideals.

Every device contains at least one swap chain.

Every municipality had at least a single chapter, which in part acted as an NGO ( non-governmental organization ) but in military affairs was part of the national chain of command.

Every chain may run in the same direction to form a parallel sheet, every other chain may run in the reverse chemical direction to form an anti parallel sheet, or the chains may be parallel and anti parallel to form a mixed sheet. The pattern of H bonding is different in the parallel and anti parallel configurations.

Every chain either has the middle tile on the outside ( O ) or the inside ( I ) of the chain ; if it is arranged so that the indicator tile is to the right of the middle tile, then the position of the ring segment on the indicator tile can either be the upper left ( UL ), upper right ( UR ), lower left ( LL ) or lower right ( LR ) corner.

Every step of the transportation chain will result in different stresses from shock and vibration.

Every chain has a relative molecular mass of approximately 80000.

Every the spark plug needed cleaning, and the chain adjustment checked, and every an oil change, breaker point check, and valve adjustment was due.

Every physical service one can think of, has its web counter part today, be it retail selling, supply chain, customer care, banking, auction and more of b2b, b2c, c2c businesses.

Every new scandal which would provide more `` copy '' for Marshall's pen would thus mean more publicity for Welch.

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 family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.

* 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 infinite game in which is a Borel subset of Baire space is determined.

Every telephone company, whether large or small, determines its own ANAC for each individual central office, which tends to perpetuate the current situation of a mess of overlapping and / or spotty areas of coverage.

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

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 year since 1972 the BVI has hosted the Spring Regatta, which is a seven-day collection of sailing races throughout the islands.

* Every real Banach algebra which is a division algebra is isomorphic to the reals, the complexes, or the quaternions.

* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.

Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.

Every computer contains an internal clock that regulates the rate at which instructions are executed and synchronizes all the various computer components.

* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".

Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.

According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".

Every argues that " the disparagement of myth in our own civilization " stems partly from objections to perceived idolatry, objections which intensified in the Reformation, both among Protestants and among Catholics reacting against the classical mythology revived during the Renaissance.

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 four years, during which an extra 24 hours have accumulated, one extra day is added to keep the count coordinated with the sun's apparent position.

Every node has a location, which is a number between 0 and 1.

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 time the boy had an injury which caused him internal or external bleeding, the Tsarina called on Rasputin, and the Tsarevich subsequently got better.

Every week before June 19, the strip focuses on Garfield's birthday, which he dreads because of his fear of getting older.

::: Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States ; If he approves he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated ...

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 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 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.