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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.
Some Related Sentences
Every and such
Every single instance of altruistic behavior need not always increase inclusive fitness ; altruistic behaviors would have been selected for if such behaviors on average increased inclusive fitness in the ancestral environment.
The older woman explains to Anne that such is the lot of a wife, and that marriage brings pain (" Every Day A Little Death ").
Every associative algebra is obviously alternative, but so too are some strictly nonassociative algebras such as the octonions.
Every information exchange between living organisms — i. e. transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate.
Every bijective function g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;
Robyn stated to Aftonbladet, a Swedish newspaper site, that she wanted to start recording a new album in the beginning of 2009 and that she will work with producers such as Kleerup (" With Every Heartbeat ") as well as Klas Åhlund who she worked with on Robyn.
She was perhaps best known for her film roles such as Minnie Castevet, Rosemary's overly solicitous neighbor in Rosemary's Baby, as the eccentric Maude in Harold and Maude and as the mother of Orville Boggs in the Clint Eastwood film Every Which Way but Loose.
Every thing depends upon the evil of the second order ; it is this which gives to such actions the character of crime, and which makes punishment necessary.
* Van Diemen's Land is often mentioned in the works of Flogging Molly, such as in the song " Every Dog Has Its Day.
Every synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.
In 1984, a tribute album titled Every Man Has a Woman was released, featuring a selection of Ono songs performed by artists such as Elvis Costello, Roberta Flack, Eddie Money, Rosanne Cash and Harry Nilsson.
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 day " technologies such as weather forecasting, remote sensing, GPS systems, satellite television, and some long distance communications systems critically rely on space infrastructure.
Every group can be trivially made into a topological group by considering it with the discrete topology ; such groups are called discrete groups.
Every system is unique to the business drivers it supports, therefore the quality attributes of each system such as fault-tolerance, backward compatibility, extensibility, reliability, maintainability, availability, security, usability, and such other – ilities will vary with each implementation.
Every type of reward that has been studied increases the level of dopamine transmission in the brain, and a variety of highly addictive drugs, including stimulants such as cocaine and methamphetamine, act directly on the dopamine system.
Every Gundam has a unique name that befits the nature of the suit and / or its origins, such as the XXXG-01W Wing Gundam, XXXG-01D Gundam Deathscythe and the XXXG-01S Shenlong Gundam.
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.
Every continent has at least one such notable institute, with North America and Europe leading the way forward.
*: Articles 19 and 23 of the constitution provides, " Every person of I-Kiribati descent ... shall ... become or have and continue to have thereafter the right to become a citizen of Kiribati .... Every person of I-Kiribati descent who does not become a citizen of Kiribati on Independence Day ... shall, at any time thereafter, be entitled upon making application in such manner as may be prescribed to be registered as a citizen of Kiribati.
Every operating system, even from the same vendor, could have radically different models of commands, operating procedures, and such facilities as debugging aids.
Every and subset
** 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.
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 separable metric space is isometric to a subset of the ( non-separable ) Banach space l < sup >∞</ sup > of all bounded real sequences with the supremum norm ; this is known as the Fréchet embedding.
* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.
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 subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.
Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable ( and therefore T4 ) and second countable.
It is more interesting that the converse also holds: Every second countable T4 space is homeomorphic to a subset of the Hilbert cube.
* Every totally disconnected compact metric space is homeomorphic to a subset of a countable product of discrete spaces.
* Every irreducible closed subset of P < sup > n </ sup >( k ) of codimension one is a hypersurface ; i. e., the zero set of some homogeneous polynomial.