All of the above requirements can be met if we define D ( P ) as an element of the tensor product of the real numbers R and the quotient space R /( Qπ ) in which all rational multiples of π are zero.

All known elementary particles, including quarks, have charges that are integer multiples of e. Therefore, one can say that the " quantum of charge " is e. In this case, one says that the " elementary charge " is three times as large as the " quantum of charge ".

All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime.

All repdigits are palindromic numbers and are multiples of repunits.

All vision carrier frequencies are on exact multiples of the channel bandwidth frequency ( 6 MHz in the case of System-M used in most countries of the Americas, other TV systems worldwide use 7 MHz or 8 MHz ).

All species are woody, with essential oils, and flower parts in multiples of four or five.

The Principia Discordia states that " All things happen in fives, or are divisible by or are multiples of five, or are somehow directly or indirectly appropriate to 5 "— this is referred to as the Law of Fives.

All quantities are specified as multiples of selected base values.

All Heronian triangles can be generated as multiples of:

All systems are based on a single stage kit, but these kits can be used in multiples ( called 2, 3 or even 4 stage ).

All of these artists and more eventually became associated with fluxus, ' either through their collaboration on multiples, inclusion in anthologies, or participation in Fluxus concerts '.

All masters use the same punishment if they witness any form of misbehaviour: the giving of lines ( a seemingly random number in multiples of a hundred, between 100 and 800 ).

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 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 divisions in the top four steps have 22 clubs each, except the Northern Premier League Division One North and Division One South which have 20 or 21 teams each, and Conference National, with 24 teams.

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 128 ASCII characters, including non-printable characters ( represented by their abbreviations ). The 95 ASCII graphic characters are numbered from 20 < sub > hexadecimal | hex </ sub > to 7E < sub > hexadecimal | hex </ sub > ( decimal 32 to 126 ).

All numbers in the Expansive Classification are ( or should be ) shelved as if in decimal order.

All but the most expensive systems used microcode to implement the instruction set, which featured 8-bit byte addressing and binary, decimal and floating-point calculations.

All Irish coins and banknotes, from the start of the Irish Free State onwards, both decimal and pre-decimal, may be exchanged for euro at the Central Bank in Dublin.

: Note: All units must be converted to the corresponding decimal ( or USCU ) units.

All binary palindromic primes except binary 11 ( decimal 3 ) have an odd number of digits ; those palindromes with an even number of digits are divisible by 3.

; White, ISBN 0-13-270232-0, 2nd printing, copyright 1999, 1995, 1991, 1987, 1982 and 1979 by Prentice Hall .</ br >( All four places, including the single decimal place, are common knowledge in the field, although a reference for the single place could not be found.

All printable ASCII characters ( decimal values between 33 and 126 ) may be represented by themselves, except "" ( decimal 61 ).

All decimal notes are legal tender except $ 1 and $ 2 notes as these have been withdrawn.

All numbers and variable contents are arbitrary precision numbers whose precision ( in decimal places ) is determined by the global variable.

All other contemporary currencies are either decimal or have no sub-units at all.