All numbers which can be obtained from the integers using a finite number of integer additions, subtractions, multiplications, divisions, and taking nth roots ( where n is a positive integer ) are algebraic.

All of the divisions were understrength.

All including 82nd and 101st Airborne divisions of the United States.

All multiples and divisions of the decimal units are factors of the power of ten, an idea first proposed by the Flemish mathematician Simon Stevin in 1586.

All of the German divisions holding front zones were relieved and an extra division brought forward as the British advances had lengthened the front line.

All of Longstreet's divisions were forced to take a long detour while approaching the enemy position, misled by inadequate reconnaissance that failed to identify a completely concealed route.

All five combatant divisions, as well as the CAOF and CAPF were disbanded by the end of 1946.

All the historical wafer fab lines are now closed but the site hosts the headquarters of many divisions ( marketing, design, industrialization ) and an important R & D center, focused on silicon and software design and fab process development.

All the eight Republican Guard divisions were involved in fighting during the Gulf War and the " Tawakalna " Division was disbanded due to losses.

All the plans relied on his divisions each having previously organised a motorised rapid reaction unit ( Kampfgruppe ) which could move speedily to meet the threat and buy time for the rest of the defenses to get in place.

All three armies would soon be reinforced: the British Secretary of State for War and the Colonies, the Duke of Newcastle, promised Raglan that the 3rd, 62nd, and 90th Regiments, would be despatched to the Crimea with a third battery train ; Canrobert, meanwhile, was promised an additional three divisions of infantry from France.

All products fall under one of these three divisions.

All teams in the league ( and by extension, the divisions of the league ) are at the same competitive level and remain so year after year.

All three divisions are profitable nowadays, although it took the golf course several years to break even.

All football players in all divisions of college football are eligible for the award, though winners usually represent Division I Football Bowl Subdivision schools.

All four divisions lay within the hundred of Salford, an ancient division of the county of Lancashire.

All clubs in the three leagues play in the Challenge Cup with the clubs in the Premier Division given byes to the third round, where they join eleven teams from the lower divisions.

All of the French possessions share the prefix F. Further divisions that are used by amateur stations are:

All the standard ornaments of the time are thoroughly presented: appoggiatura, messa di voce, eight kinds of trills, passaggi ( divisions ), and portamento.

All five of the full army groups ( meaning a group of divisions similar in size to an army, not a group of armies ) were made up of volunteer recruits, which included the famous Pals ' Battalions.

All models also featured a revised " Astro Ventilation " system utilizing vents in the doorjams that replaced the troublesome 1971 version that used vents in the trunklid and turned out to be a major source of complaints to Chevy ( and other GM divisions ) dealers from customers.

All existing divisions were then assigned as appropriate.

All four divisions composed mostly of Indian Sepoys.

All of the leagues have a Premier Division of 22 teams ( Level 7 ) with two parallel divisions each of 22 teams split by region below ( Level 8 ).

All application-level protocols, including the infrastructure protocols NBP, RTMP and ZIP, were built on top of DDP.

All cross stitch fabrics are technically " evenweave ", it refers to the fact that the fabric is woven to make sure that there are the same number of threads in an inch both left to right and top to bottom ( vertically and horizontally ).

All phonetic keystrokes may be accomplished by one and two-key chords of the home keys on the top row.

All ancient doors were hung by pivots at the top and bottom of the hanging stile which worked in sockets in the lintel and sill, the latter being always in some hard stone such as basalt or granite.

A second single, the double A-sided single " Two Doors Down "/" It's All Wrong, But It's All Right " also topped the country singles chart and crossed over to the pop top twenty.

All the layers are stacked, one above the next, in any desired order ; and the bottom layer is usually rendered as a base in the resultant image, with each higher layer being progressively rendered on top of the previously composited of layers, moving upward until all layers have been rendered into the final composite.

All three stressed that the mouthpiece should be placed higher on the top lip for a more free vibration of the lips.

All top officials reported to Hitler and followed his basic policies, but they had considerable autonomy on a daily basis.

All citizens of Haiti, regardless of skin color, to be known as " Black " ( this was an attempt to eliminate the multi-tiered racial hierarchy that had developed in Haiti, with full or near full-blooded Europeans at the top, various levels of light to brown skin in the middle, and dark skinned " Kongo " from Africa at the bottom ).

All S models have arched top bodies.

All eight Ivy League institutions place within the top sixteen of the U. S. News & World Report college and university rankings, including the top four schools and five of the top nine.

All concepts, except the top concept ( usually THING ), must have at least one super class.

All ten NDC members were ranked within the top twenty on September 5, and all but one occupied the top twenty at the fiftieth anniversary of National Foundation Day on September 9.

All calculations show large heating ( up to 80 ° C ) at the top of the smoke layer at about 10 km ; this implies a substantial modification of the circulation there and the possibility of advection of the cloud into low latitudes and the southern hemisphere.

Ontario's Sum 41 reached the Canadian top ten with its 2001 debut album, All Killer No Filler, which eventually went platinum in the United States.

All other two pairs keep together with any ace top, else split the pairs.

In the 2002 Sight & Sound directors ' poll, Tarantino revealed his top 12 films: The Good, the Bad and the Ugly ; Rio Bravo ; Taxi Driver ; His Girl Friday ; Rolling Thunder ; They All Laughed ; The Great Escape ; Carrie ; Coffy ; Dazed and Confused ; Five Fingers of Death ; and Hi Diddle Diddle.

All six flavors of quark have since been observed in accelerator experiments ; the top quark, first observed at Fermilab in 1995, was the last to be discovered.

Two Elvis Presley records made the R & B top five in 1957: " Jailhouse Rock "/" Treat Me Nice " at # 1, and " All Shook Up " at # 5, an unprecedented acceptance of a non-African American artist into a music category known for being created by blacks.

All gaming machines in Victoria have an information screen accessible to the user by pressing the ' i key ' button, showing the game rules, paytable, return to player percentage, and the top and bottom five combinations, with the odds shown.

All Cetacea have forelimbs modified as fins, a tail with horizontal flukes, and nasal openings ( blowholes ) on top of the head.