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Every one of the infinitely many vertices of G can be reached from v < sub > 1 </ sub > with a simple path, and each such path must start with one of the finitely many vertices adjacent to v < sub > 1 </ sub >.
Some Related Sentences
Every and one
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.
** 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 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 week Holbrook writes the story line for the next three weeks for one of his strips and draws the next three weeks ' worth of strips for another.
Every one of us has been passing through days of anxiety ; we cannot, however, feel that peace has been established, but that we have nothing but an armistice in a state of war.
* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.
Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.
Every person should be identified uniquely as resident in one place but where they happen to be on census day, their de facto residence, may not be the best place to count them.
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 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.
In Norse mythology, Draupnir ( Old Norse " the dripper ") is a gold ring possessed by the god Odin with the ability to multiply itself: Every ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original.
Every system must have a class designated as " root ", with one of its creation procedures designated as " root procedure ".
Every other aspect of film making originated in a different medium than film ( photography, art direction, writing, sound recording ), but editing is the one process that is unique to film.
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 and infinitely
Cantor points out that his constructions prove more — namely, they provide a new proof of Liouville's theorem: Every interval contains infinitely many transcendental numbers.
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
Every process involving charged particles emits infinitely many coherent photons of infinite wavelength, and the amplitude for emitting any finite number of photons is zero.
Every real number x is surrounded by an infinitesimal " cloud " of hyperreal numbers infinitely close to it.
This is up to isomorphism the only indecomposable module over R. Every left R-module is a direct sum of ( finitely or infinitely many ) copies of this module K < sup > n </ sup >.
Every infinitely divisible probability distribution corresponds in a natural way to a Lévy process, i. e., a stochastic process
Every and many
Every pitch in the game brought forth a howl from the enraptured audience and every fly ball the visitors dropped ( and because their right fielder was still a little fuzzy from drink, they dropped many ) called forth yelps of derision.
George Every discusses the connection between the cosmic center and Golgotha in his book Christian Mythology, noting that the image of Adam's skull beneath the cross appears in many medieval representations of the crucifixion.
Every Andalusian region or comarca has its own variety of this popular food so there are many types of gazpacho.
A Girl in Every Port is considered by film scholars to be the most important film of Hawks's silent career because it is his first film to introduce many of the Hawksian themes and characters that would continue until his final films.
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 product of ( arbitrarily many ) profinite groups is profinite ; the topology arising from the profiniteness agrees with the product topology.
Earlier books such as What Every Girl Should Know ( Margaret Sanger, 1920 ) and A Marriage Manual ( Hannah and Abraham Stone, 1939 ) had broken the silence in which many people, women in particular, had grown up in.
Every Saturday morning it hosts a large outdoor market or " mercadillo ", where many gypsies come and sell their wares of fruits and vegetables, clothes and shoes, and other odds and ends.
: Every integer which can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units.
Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.
Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.
Every monad arises from some adjunction — in fact, typically from many adjunctions — in the above fashion.
Every time, there will be many famous singers who perform on the stage that is set up for the New Year Celebration.
Every pre-abelian category is of course an additive category, and many basic properties of these categories are described under that subject.
Every two years, the museum hosts the Whitney Biennial, an international art show which displays many lesser-known artists new to the American art scene.