A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f ( s ) is an element of s. With this concept, the axiom can be stated:

With large sets, it becomes necessary to use more sophisticated mathematics to find the number of combinations.

With longer sets ( more than ~ 40 people ) this would require long enough sets that the caller will usually only run the dance all the way around on ( rare ) non equal-turn dances.

With this knowledge and a pair of glasses given to him as a gift by Wonder Woman, ' Clark ' regains his humanity, and sets out to become a hero again by re-fertilizing the irradiated fields of Kansas.

With this communication Epaphroditus sets out on his homeward journey ( 3. 28-29 ).

With Rigoletto, Verdi sets up his original idea of musical drama as a cocktail of heterogeneous elements, embodying social and cultural complexity, and beginning from a distinctive mixture of comedy and tragedy.

With the rise of the DVD video format, box sets featuring season or series runs of television series have become an increasingly important retail item.

With the advent of flat-panel televisions, set-top boxes are now deeper in profile than the tops of most modern TV sets.

With the code he gets from Freeman, he sets up an identity as an Army Major, with Kate as his prisoner.

With prom fast approaching, Sue sets Carrie up with her handsome boyfriend, Tommy Ross.

With the help of Glass, Nettles sets out to find and stop Swann ... and maybe exorcise the demons from his own tortured past.

With the help of Nick and some of the other inmates such as Twitch ( Ricardo " Kurupt " Brown ) and Little Joe ( Michael " Bear " Taliferro ), Sascha sets out to rescue June and bring Donny down, before Alcatraz becomes everyone's final resting place.

With glamorous costumes and sets, a musical score by Stephen Sondheim, and Jean-Paul Belmondo in the title-role, it was seen as Resnais's most commercial film to date, but its complex narrative structure showed clear links with some of the formal preoccupations of his earlier films.

With the rising tide, the submarine frees itself, and the Russian captain ( Theodore Bikel ) sets out in search of his missing men.

With every year that passes the department sets records on their selling and the loving donations that the public of Womelsdorf give so much.

With the advent of " modern bodybuilding " ( where bodybuilders became more massive than ever before ) by the early 1990s, he ultimately modified that routine until there were fewer working sets, and more days of rest.

With younger model builders in mind, many theme sets were also introduced, including a " Construction and Agricultural " series, " Space " models and " Dynamic " sets.

With the introduction of the FD Trinitron, Sony also introduced a new industrial style, leaving the charcoal colored sets introduced in the 1980s for a new silver styling.

With Berle at the helm, Texaco Star Theater was credited heavily with driving American television set sales heavily ; the number of TV sets sold during Berle's run on the show was said to have grown from 500, 000 his first year on the tube to over 30 million when the show ended in 1956.

With the transition to Williams, the show recognized its past in its opening seconds, with small photos of past anchors and sets and the voices of John Cameron Swayze, Huntley, Brinkley, Chancellor, and Brokaw, as well as an orchestral version of the " G-E-C " NBC Chimes, before going into the opening headlines read by Williams.

Jim Messina, President Obama's campaign manager, stated: " With so much at stake, we can't allow for two sets of rules in this election whereby the Republican nominee is the beneficiary of unlimited spending and Democrats unilaterally disarm ".

With this, the Officer frees the Condemned and sets up the machine for himself, with the words " Be Just " to be written on him.

With his tiny minions, and his trusty shrink ray, he began turning St. Canard's monuments into miniature props for his golf course.

With the decline of the mining industry, pit props are no longer imported and the Timber Pond is now a marina trading under the name Goole Boathouse.

With the aid of a wide range of specially made ' props ' – dolls, various prosthetic limbs, stiletto heels, dildos and an occasional confidante – Pierre Molinier focused upon his own body as the armature for a constructive form that ultimately produced a large body of photographic work.

With one set and low-rent props ( is that an ordinary laptop inside the nuclear briefcase " football?

" With money earned from winning matches in story mode and playing the Survival mode, players can purchase unlockable characters, clothing, wrestling moves, props, tattoos, weapons, and venues.

With the cast and crew suffering from burnout and lack of resources, the season finale The Invasion of Time was completed largely by virtue of it having been written to make use of preexisting sets, props, and costumes.

With him were Hank Maguire, Luis Hernandez, and Luis's son Pedro.

This arrangement was for Copernicus literally monstrous: `` With ( the Ptolemaists ) it is as though an artist were to gather the hands, feet, head and other members for his images from divers models, each part excellently drawn, but not related to a single body ; ;

To Serenissimus such tribes as the Cossacks of the Don or those ex-bandits the Zaporogian Cossacks ( in whose islands along the lower Dnieper the Polish novelist Sienkiewicz would one day place With Fire And Sword ) were just elements for enforced resettlement in, say, Bessarabia, where, as `` the faithful of the Black Sea borders '', he could use their presence as bargaining points in the Czarina's territorial claims against Turkey.

With their facile generalizations about the United States, these mediocrities, as they often were, had been great successes.

With the birth of the Turkish Republic after the First World War, St. Sophia became a museum, and the ancient mosaics, which were plastered over by the Moslems, whose religion forbids pictures in holy places, have been restored.

With completion of filling, net-like anastomoses were noted to be present between these separately derived branches.

With the exception of treaty-making, foreign relations were historically concerned for the most part with conditions of short or at least measurable duration.

With these completed and ice gone from the St. Peter's River ( present-day Minnesota river ) their 250 bushels of wheat, 100 bushels of oats and barley and 30 bushels of peas and some chickens were loaded onto the flat-bottomed boats and rowed up the river to Big Stone Lake, across into Lake Traverse, and down the Red.

With the divinities present and our souls in place, we were wished health, happiness, and power.

With four younger children at home, Lucy stepped into her mother's role, and even after the brothers and sisters were grown, she was her father's comfort and stay until he died in 1879.

With such a dream arising, at least in part, from the Protestant heritage of the United States and built into the foundations of the nation, it is not surprising that many efforts were made to give it concrete expression.

With Britain looking inward, overseas problems were neglected and the baton was passed on to the United States.

With one corner of his mind he knew that they were saying nothing, just expressing the euphoria of a drug so powerful that the known universe had forbidden it.

The term became popular again in Australia first, when George Giffen, in his memoirs ( With Bat and Ball, 1899 ), used the term as if it were well known.

With J. J. Thomson's discovery of the electron in 1897, it became clear that atoms were not the smallest building blocks of nature, but were rather composite particles.

With the 1994 passage of the North American Free Trade Agreement, the following words were used to label the United States Section of that organization: in French, étatsunien ; in Spanish, estadounidense.

With more ardor than depth, Ibn Yasin's arguments were disputed by his audience.

With everyone running in different directions, some local businessmen worked out a deal and were awarded an AFL franchise on June 7, 1965, contingent upon acquiring exclusive stadium rights from city officials.

With the rise of education, cheap newspapers and cheap printing, modern concepts of fame and celebrity began to develop, and the beneficiaries of this were not slow to cash in on this by producing autobiographies.

With the lack of international competition, representative matches between state teams were regarded with great importance.

With limited supplies, the cultivation of food was imperative, but the soils around Sydney were poor, the climate was unfamiliar, and moreover very few of the convicts had any knowledge of agriculture.

With the end of western Roman power, the islands, to the extent that they were governed at all, were part of territories of Goths, Vandals, Saracens, before the Normans fortified Favignana in 1081.

Among other composers who set Housman songs were John Ireland ( song cycle, Land of Lost Content ), Michael Head ( e. g. ' Ludlow Fair '), Graham Peel ( a famous version of ' In Summertime on Bredon '), Ian Venables ( Songs of Eternity and Sorrow ), and the American Samuel Barber ( e. g. ' With rue my heart is laden ').