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Number

Specialty Definition: Number

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Specialty Definition: Département

(From Wikipedia, the free Encyclopedia)

The départements (or departments) are administrative units of France, roughly analogous to British counties and now grouped into 22 metropolitan and four overseas régionss. They are subdivided into 342 arrondissements. Départements are also found in Côte d'Ivoire.

Administrative role

Each département is administered by a Conseil Général elected for six years, and by a préfet appointed by the French government and assisted by one or more sous-préfets based in district centres outside the departmental capital. An administrative reform in 1982 transferred some of the préfet's powers to the president of the Conseil Général.

The capital city of a département bears the title of préfecture. Départements are divided into one to five arrondissements. The capital city of an arrondissement is called the sous-préfecture. The civil servant in charge is the sous-préfet.

The départements sub-divide into communes, governed by municipal councils. France (as of 1999) had 36,779 communes.

Most of the départements have an area of around 4,000-8,000 km² and a population between 250,000 and a million. The largest in terms of area is Gironde (10,000 km²) and the smallest the city of Paris (105 km² excluding the suburbs, now organised in adjacent départements). The most populous is Nord (2,550,000) and the least populous Lozère (74,000).

The départements are numbered: their two-digit numbers appear in postal codes and on car number-plates. Note that there is no number 20, but 2A and 2B instead. Note also that the two-digit code "98" is used by Monaco. Together with the ISO 3166-1 country code FR the numbers form the ISO 3166-2 country subdivision codes for the metropolitain departments. The overseas departments get two letters for the ISO 3166-2 code.

History

Départements were created on January 15, 1790 by the Constituent Assembly to replace the country's former provinces with a more rational structure. They were also designed to deliberately break up France's historical regions in an attempt to erase cultural differences and build a more homogeneous nation. Most départements are named after the area's principal river(s) or other physical features.

The number of départements rose from an initial 83 to 130 by 1810 with the territorial gains of the Republic and of the Empire (see Provinces of the Netherlands for the annexed Dutch departements), but they were reduced again to 86 with Napoleon I's defeat in 1814-1815. Three more were added with the acquisition of Nice and Savoy in 1860. The numbering was estabished on the alphabetical order of those 89 départements.

Three were yielded to Germany in Alsace-Lorraine in 1871 (Haut-Rhin, Bas-Rhin and Moselle) re-joined France in 1919.

Reorganisations of the Paris region (1968) and the division of Corsica (1975) have added a further seven départements, raising the total to one hundred - including the four overseas départements d'outre-mer (DOM) of Guyane (French Guiana) in South America, Guadeloupe and Martinique in the Caribbean Sea, and Réunion in the Indian Ocean.

Map and list of départements

French régions and départements

Number	Département	Préfecture
01	Ain	Bourg-en-Bresse
02	Aisne	Laon
03	Allier	Moulins
04	Alpes-de-Haute-Provence	Digne
05	Hautes-Alpes	Gap
06	Alpes-Maritimes	Nice
07	Ardèche	Privas
08	Ardennes	Charleville-Mézières
09	Ariège	Foix
10	Aube	Troyes
11	Aude	Carcassonne
12	Aveyron	Rodez
13	Bouches-du-Rhône	Marseille
14	Calvados	Caen
15	Cantal	Aurillac
16	Charente	Angoulême
17	Charente-Maritime	La Rochelle
18	Cher	Bourges
19	Corrèze	Tulle
2A	Corse-du-Sud	Ajaccio
2B	Haute-Corse	Bastia
21	Côte-d'Or	Dijon
22	Côtes-d'Armor	Saint-Brieuc
23	Creuse	Guéret
24	Dordogne	Périgueux
25	Doubs	Besançon
26	Drôme	Valence
27	Eure	Evreux
28	Eure-et-Loir	Chartres
29	Finistère	Quimper
30	Gard	Nîmes
31	Haute-Garonne	Toulouse
32	Gers	Auch
33	Gironde	Bordeaux
34	Hérault	Montpellier
35	Ille-et-Vilaine	Rennes
36	Indre	Châteauroux
37	Indre-et-Loire	Tours
38	Isère	Grenoble
39	Jura	Lons-le-Saunier
40	Landes	Mont-de-Marsan
41	Loir-et-Cher	Blois
42	Loire	Saint-Etienne
43	Haute-Loire	Le Puy
44	Loire-Atlantique	Nantes
45	Loiret	Orléans
46	Lot	Cahors
47	Lot-et-Garonne	Agen
48	Lozère	Mende
49	Maine-et-Loire	Angers
50	Manche	Saint-Lô
51	Marne	Châlons-en-Champagne
52	Haute-Marne	Chaumont
53	Mayenne	Laval
54	Meurthe-et-Moselle	Nancy
55	Meuse	Bar-le-Duc
56	Morbihan	Vannes
57	Moselle	Metz
58	Nièvre	Nevers
59	Nord	Lille
60	Oise	Beauvais
61	Orne	Alençon
62	Pas-de-Calais	Arras
63	Puy-de-Dôme	Clermont-Ferrand
64	Pyrénées-Atlantiques	Pau
65	Hautes-Pyrénées	Tarbes
66	Pyrénées-Orientales	Perpignan
67	Bas-Rhin	Strasbourg
68	Haut-Rhin	Colmar
69	Rhône	Lyon
70	Haute-Saône	Vesoul
71	Saône-et-Loire	Mâcon
72	Sarthe	Le Mans
73	Savoie	Chambéry
74	Haute-Savoie	Annecy
75	Paris	Paris
76	Seine-Maritime	Rouen
77	Seine-et-Marne	Melun
78	Yvelines	Versailles
79	Deux-Sèvres	Niort
80	Somme	Amiens
81	Tarn	Albi
82	Tarn-et-Garonne	Montauban
83	Var	Toulon
84	Vaucluse	Avignon
85	Vendée	La Roche-sur-Yon
86	Vienne	Poitiers
87	Haute-Vienne	Limoges
88	Vosges	Epinal
89	Yonne	Auxerre
90	Territoire-de-Belfort	Belfort
91	Essonne	Evry
92	Hauts-de-Seine	Nanterre
93	Seine-Saint-Denis	Bobigny
94	Val-de-Marne	Créteil
95	Val-d'Oise	Pontoise
971	Guadeloupe 1	Basse-Terre
972	Martinique 1	Fort-de-France
973	Guyane 1	Cayenne
974	La Réunion 1	Saint-Denis
The following are not départments (see notes):
986	Wallis and Futuna 2	Mata-Utu
987	French Polynesia2	Papeete
975	Saint Pierre and Miquelon3	Saint Pierre
976	Mayotte3	Mamoutzou
988	New Caledonia 3	Noumea

Notes:

1. The overseas departments are former colonies outside France that now enjoy a status similar to European or metropolitan France. They are part of France and of the EU. Each of them constitutes a région at the same time.
2. Beyond these there are also three "overseas territories" (French: territoires d'outre-mer, or TOM) that are part of France but not of the EU. They are: French Polynesia, Wallis and Futuna and the French Southern and Antarctic Territories.
3. Furthermore there are three separate special status territories (French: collectivites territorialles), also part of France but not of the EU: Saint Pierre and Miquelon, Mayotte and New Caledonia. New Caledonia used to be a TOM.

Finally, France maintains control over a number of small islands in the Indian Ocean and the Pacific.

Former départements

(incomplete list)

• Seine
• Seine-et-Oise
• French départements in the Netherlands
• French départements in Algeria
  • 91 Algiers
  • 92 Oran
  • 93 Constantine
• The 130 départements of the Napoleonic Empire

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Département."

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Grammatical number

(From Wikipedia, the free Encyclopedia)

In many languages the parts of speech are inflected differently depending on whether they are related to a noun of which there's only one instance (singular), or several (plural). Several languages also have a dual grammatical number that expresses the existence of precisely two instances of the noun, and a collective number that expresses the whole class of the nouns. Other languages (one of which is English) treat dual nouns as simply plural. Some other languages have a trial number for three or a paucal number, expressing few -- but not many -- instances of a noun, which is separate from the singular or plural numbers. Also, some languages have of collective nouns (e.g. "mankind") that are declined either as singular or plural, but semantically express multitude.

In English the following are irregular examples:

• house (singular), houses (plural)
• mouse (singular), mice (plural)
• I (singular), we (plural)

And one regular example:

• encyclopedia (singular), encyclopedias (plural)

Non-borrowed English irregular nouns come in several forms:

Some voice a final fricative when in plural:

• knife, knives (f>v)
• mouth, mouths (T>D)
• house, houses, (unique plural, s>z)

These plural are distinct in pronounciation from the possessive. There is also a trend in some areas to regularize some of these nouns.

Survivors of the Old English weak masculine declination add -en:

• ox, oxen
• auroch, aurochen (archaic)

Other -en adders are irregular due to different reasons:

• child, children
• eye, eyen (rare)
• cow, kine (rare)
• brother, brethren (or brothers)

Some nouns have no plural, or are identical when plural and singular:

• moose
• sheep
• fish (or fishes)
• species

Pronouns are irregular precisely because they are so common:

• I, we
• you
• he she it, they

Some nouns are rather transparently irregular because they undergo the process of umlaut:

man, men foot, feet mouse, mice

There are several different kinds depending in the starting and ending vowel, but generally, they converge on /i/.

Most of these nouns are also umlautized in the other Germanic languages.

The (regular) English noun plural marker, -s, has three variants:

• -/s/ next to a voiceless consonant other than a fricative
• -/z/ next to a voiced sound other than a fricative, or a vowel
• -/@z/ or -/Iz/ next to /s/, /z/, /S/, /Z/, /tS/ and /dZ/ (the choice of vowel depending on dialect)

In Slovene more complicated:

• babarija (old wives tale) (singular), babariji (two old wives tales) (dual), babarije (three old wives tales)
• hiša (house) (singular), hiši (two houses) (dual), tri hiše (three houses) (plural), šest hiš (six houses) (plural)
• miš (mouse) (singular), miši (two or three mice) (dual := plural)
• jaz (I) (singular), midva/midve (we) (dual + [Masculine/Feminine gender), mi/me (we) (plural [Ma/Fe gender])
• vrata (one door) (singular), dvoje vrat (two doors (dual), tri vrata (three doors (plural), [plural noun with different or same form]
• babine (afterbirth period) (archaic meaning) (singular), babini (two afterbirth periods) (dual), babine (three afterbirth periods), [plural noun with different or same form]
• človeštvo (mankind) (singular), človeštvi (two mankind) (dual), človeštva (three mankind), [collective noun with different form]
  • This kind of examples are very often used incorrecty (even in published or electronic dictionaries).

In Hebrew, one can similarly say:

• sefer (book) (singular), sfarim (books) (plural)
• yom (day) (singular), yamim (days) (plural), but yomaim (two days) (dual)

In terms of pronunciation, however, the majority of nouns (and adjectives) in French are not actually declined for number. The -s suffix is not actually pronounced unless the next word starts with a vowel (this is called liaison) and thus does not really show anything; the plural article or other word is the real indicator of plurality. However, plurals still exist in French because irregular nouns, such as those that end in -l such as cheval, horse, form plurals in a different way. Cheval is pronounced [S@val], cheveaux is pronounced [S@vo], and this is a real showing of number differences. The same is true for adjectives.

Not only nouns can be declined by number. In many languages, adjectives are declined according to the number of the noun they modify. For example, in French, one may say un arbre vert (a green tree), and des arbres verts ([some] green trees). The word vert (green), in the singular, becomes verts for the plural (unlike English green, which remains green).

In many languages, verbs are conjugated by number as well. Using French as an example again, one says je vois (I see), but nous voyons (we see). The verb voir (to see) in the first person changes from vois in singular, to voyons in plural. In English this occurs in the third person (she runs, they run) but not first or second.

Normally verbs agree with their subject noun in number. But in Ancient Greek and Sanskrit neuter plurals took a singular verb. In English nouns collectively referring to people may take singular verbs, as the committee are meeting; use of this varies by dialect and level of formality.

Other qualifiers may also agree in number. The English article the does not, the demonstratives this, that do, becoming these, those, and the article a, an is omitted or changed to some in the plural. In French and German the definite articles have gender distinctions in the singular but not the plural. In Portuguese the indefinite article um, uma has plural forms uns, umas.

See grammar, mass noun, collective noun.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Grammatical number."

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Integer

(From Wikipedia, the free Encyclopedia)

The integers consist of the natural numbers (0, 1, 2, ...) and their negatives (-1, -2, -3, ...; -0 is equal to 0 and therefore not included as a separate integer). The set of all integers is usually denoted by Z (or Z in blackboard bold, ), which stands for Zahlen (German for "numbers").

Integers can be added and subtracted, multiplied, and compared. Introducing the negative integers makes it possible to solve all equations of the form

a + x = b

(where a and b are constant natural numbers) for the unknown x; if x is constrained to the natural numbers, only some of these equations are solvable.

Mathematicians express the fact that all the usual laws of arithmetic are valid in the integers by saying that (Z, +, *) is a commutative ring.

Z is a totally ordered set without upper or lower bound. The ordering of Z is given by

... < -2 < -1 < 0 < 1 < 2 < ...

We call an integer positive if it is greater than zero; zero itself is not considered to be positive. The order is compatible with the algebraic operations in the following way:

1. if a < b and c < d, then a + c < b + d
2. if a < b and 0 < c, then ac < bc

Like the natural numbers, the integers form a countably infinite set.

The integers do not form a field since for instance there is no integer x such that 2x = 1. The smallest field containing the integers is the rational numbers.

An important property of the integers is division with remainder: given two integers a and b with b≠0, we can always find integers q and r such that

a = b q + r

and such that 0 <= r < |b| (see absolute value). q is called the quotient and r is called the remainder resulting from division of a by b. The numbers q and r are uniquely determined by a and b. This shows that the greatest common divisor of two integers can always be written as a sum of multiples of the two numbers, and makes the Euclidean algorithm for computing greatest common divisors possible.

All of this can be abbreviated by saying that Z is a Euclidean domain. This implies that Z is a principal ideal domain and that whole numbers can be written as products of primes in an essentially unique way. This is the fundamental theorem of arithmetic.

The branch of mathematics which studies the integers is called number theory.

An integer is often one of the primitive datatypes in computer languages. Note, however, that a computer can only represent a subset of all mathematical integers, given that computers are finite machines. Integer datatypes are typically implemented using a fixed number of bits, and even variable-length representations eventually run out of storage space when trying to represent especially large numbers. See integer (computer science) for more detailed discussion.

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Integer."

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List of elements by number

(From Wikipedia, the free Encyclopedia)

List of elements by number

See also: periodic table, list of elements by name, list of elements by symbol

No.	Name	Sym.
1	hydrogen	H
2	helium	He
3	lithium	Li
4	beryllium	Be
5	boron	B
6	carbon	C
7	nitrogen	N
8	oxygen	O
9	fluorine	F
10	neon	Ne
11	sodium	Na
12	magnesium	Mg
13	aluminum	Al
14	silicon	Si
15	phosphorus	P
16	sulfur	S
17	chlorine	Cl
18	argon	Ar
19	potassium	K
20	calcium	Ca
21	scandium	Sc
22	titanium	Ti
23	vanadium	V
24	chromium	Cr
25	manganese	Mn
26	iron	Fe
27	cobalt	Co
28	nickel	Ni
29	copper	Cu
30	zinc	Zn
31	gallium	Ga
32	germanium	Ge
33	arsenic	As
34	selenium	Se
35	bromine	Br
36	krypton	Kr
37	rubidium	Rb
38	strontium	Sr
39	yttrium	Y
40	zirconium	Zr
41	niobium	Nb
42	molybdenum	Mo
43	technetium	Tc
44	ruthenium	Ru
45	rhodium	Rh
46	palladium	Pd
47	silver	Ag
48	cadmium	Cd
49	indium	In
50	tin	Sn
51	antimony	Sb
52	tellurium	Te
53	iodine	I
54	xenon	Xe
55	cesium	Cs
56	barium	Ba
57	lanthanum	La
58	cerium	Ce
59	praseodymium	Pr
60	neodymium	Nd
61	promethium	Pm
62	samarium	Sm
63	europium	Eu
64	gadolinium	Gd
65	terbium	Tb
66	dysprosium	Dy
67	holmium	Ho
68	erbium	Er
69	thulium	Tm
70	ytterbium	Yb
71	lutetium	Lu
72	hafnium	Hf
73	tantalum	Ta
74	tungsten	W
75	rhenium	Re
76	osmium	Os
77	iridium	Ir
78	platinum	Pt
79	gold	Au
80	mercury	Hg
81	thallium	Tl
82	lead	Pb
83	bismuth	Bi
84	polonium	Po
85	astatine	At
86	radon	Rn
87	francium	Fr
88	radium	Ra
89	actinium	Ac
90	thorium	Th
91	protactinium	Pa
92	uranium	U
93	neptunium	Np
94	plutonium	Pu
95	americium	Am
96	curium	Cm
97	berkelium	Bk
98	californium	Cf
99	einsteinium	Es
100	fermium	Fm
101	mendelevium	Md
102	nobelium	No
103	lawrencium	Lr
104	rutherfordium	Rf
105	dubnium	Db
106	seaborgium	Sg
107	bohrium	Bh
108	hassium	Hs
109	meitnerium	Mt
110	darmstadtium	Ds
111	unununium	Uuu
112	ununbium	Uub
114	ununquadium	Uuq

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "List of elements by number."

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List of Pokémon

(From Wikipedia, the free Encyclopedia)

Japanese names are given in parentheses where they differ from English. The numbers are for Pokémon Gold and Silver.

1. Bulbasaur (Fushigidane)
2. Ivysaur (Fushigisou)
3. Venusaur (Fushigibana)
4. Charmander (Hitokage)
5. Charmeleon (Lizardo)
6. Charizard (Lizardon)
7. Squirtle (Zenigame)
8. Wartortle (Kameil)
9. Blastoise (Kamex)
10. Caterpie
11. Metapod (Transel)
12. Butterfree
13. Weedle (Beedle)
14. Kakuna (Cocoon)
15. Beedrill (Spear)
16. Pidgey (Poppo)
17. Pidgeotto (Pidgeon)
18. Pidgeot
19. Rattata (Koratta)
20. Raticate (Ratta)
21. Spearow (Onisuzume)
22. Fearow (Onidrill)
23. Ekans (Arbo)
24. Arbok
25. Pikachu
26. Raichu
27. Sandshrew (Sand)
28. Sandslash (Sandpan)
29. Nidoran-F
30. Nidorina
31. Nidoqueen
32. Nidoran-M
33. Nidorino
34. Nidoking
35. Clefairy (Pippi)
36. Clefable (Pixy)
37. Vulpix (Rokon)
38. Ninetails (Kyukon)
39. Jigglypuff (Purin)
40. Wigglytuff (Pukurin)
41. Zubat
42. Golbat
43. Oddish (Nazonokusa)
44. Gloom (Kusaihana)
45. Vileplume (Rafracia)
46. Paras
47. Parasect
48. Venonat (Konpan)
49. Venomoth (Morphon)
50. Diglett (Digda)
51. Dugtrio
52. Meowth (Nyase)
53. Persian
54. Psyduck (Koduck)
55. Golduck
56. Mankey
57. Primeape (Okorizaru)
58. Growlithe (Gardie)
59. Arcanine (Windie)
60. Poliwag (Nyoromo)
61. Poliwhirl (Nyorozon)
62. Poliwrath (Nyorobon)
63. Abra (Casey)
64. Kadabra (Yunghelor)
65. Alakazam (Fudin)
66. Machop (Wanriki)
67. Machoke (Goriki)
68. Machamp (Kairiki)
69. Bellsprout (Madatsubomi)
70. Weepinbell (Utsudon)
71. Victreebel (Utsubot)
72. Tentacool (Menokurage)
73. Tentacruel (Dokokurage)
74. Geodude (Ishitsubute)
75. Graveler (Golon)
76. Golem (Golonya)
77. Ponyta
78. Rapidash (Gallop)
79. Slowpoke (Yadon)
80. Slowbro (Yadoran)
81. Magnemite (Coil)
82. Magneton (Reacoil)
83. Farfetch'd (Kamonegi)
84. Doduo (Dodo)
85. Dodrio
86. Seel (Pawwow)
87. Dewgong (Jugon)
88. Grimer (Betbeter)
89. Muk (Betbeton)
90. Shellder
91. Cloyster (Parshen)
92. Gastly (Ghos)
93. Haunter (Ghost)
94. Gengar
95. Onix (Iwake)
96. Drowzee (Sleep)
97. Hypno (Sleeper)
98. Krabby (Crab)
99. Kingler
100. Voltorb (Biriridama)
101. Electrode (Marumain)
102. Exeggcute (Tamatama)
103. Exeggcutor (Nassie)
104. Cubone (Karakara)
105. Marowak (Garagara)
106. Hitmonlee (Sawamurer)
107. Hitmonchan (Ebiwarer)
108. Lickitung (Beroringa)
109. Koffing (Dogaasu)
110. Weezing (Matadogas)
111. Rhyhorn (Psyhorn)
112. Rhydon (Psydon)
113. Chansey (Lucky)
114. Tangela (Monjara)
115. Kangaskhan (Garura)
116. Horsea (Tattsu)
117. Seadra
118. Goldeen (Tosakinto)
119. Seaking (Azumaou)
120. Staryu (Hitodeman)
121. Starmie (Sutaamii)
122. Mr. Mime (Barrierd)
123. Scyther (Strike)
124. Jynx (Rougela)
125. Electabuzz (Elebuu)
126. Magmar (Boober)
127. Pinsir (Kiros)
128. Tauros (Kentauros)
129. Magikarp (Koiking)
130. Gyarados
131. Lapras
132. Ditto (Metamon)
133. Eevee (Iibui)
134. Vaporeon (Showers)
135. Jolteon (Thunders)
136. Flareon (Booster)
137. Porygon
138. Omanyte (Omnite)
139. Omastar (Omster)
140. Kabuto
141. Kabutops
142. Aerodactyl (Ptera)
143. Snorlax (Kabigon)
144. Articuno (Freezer)
145. Zapdos (Thunder)
146. Moltres (Fire)
147. Dratini (Miniryu)
148. Dragonair (pokemon) (Hakuryu)
149. Dragonite (Kairyu)
150. Mewtwo
151. Mew
152. Chikorita
153. Bayleef
154. Meganium
155. Cyndaquil (Hinoarashi)
156. Quilava (Magumarashi)
157. Typhlosion (Bakufuun)
158. Totodile (Waninoko)
159. Croconaw (Arigeitsu)
160. Feraligatr (Oudairu)
161. Sentret (Otachi)
162. Furret (Ootachi)
163. Hoothoot
164. Noctowl (Yorunozuko)
165. Ledyba
166. Ledian
167. Spinarak (Itomaru)
168. Ariados
169. Crobat
170. Chinchou (Chonchi)
171. Lanturn
172. Pichu
173. Cleffa (Pii)
174. Igglybuff (Pupurin)
175. Togepi
176. Togetic (Togechikku)
177. Natu (Neiti)
178. Xatu (Netio)
179. Mareep
180. Flaaffy (Mokoko)
181. Ampharos (Denryuu)
182. Bellossum (Kireihana)
183. Marill
184. Azumarill (Mariruri)
185. Sudowoodo (Usokkii)
186. Politoed (Nyorotono)
187. Hoppip (Hanekko)
188. Skiploom (Popokko)
189. Jumpluff (Watakko)
190. Aipom
191. Sunkern (Himanattsu)
192. Sunflora (Kimawari)
193. Yanma (Yanyanma)
194. Wooper (Upaa)
195. Quagsire (Nuoo)
196. Espeon (Eefi)
197. Umbreon (Burakki)
198. Murkrow (Yamikarasu)
199. Slowking (Yadokingu)
200. Misdreavus (Muuma)
201. Unown (Annon)
202. Wobbuffet (Sounansu)
203. Girafarig (Kirinriki)
204. Pineco (Kunugidama)
205. Forretress (Foretosu)
206. Dunsparce (Nokotchi)
207. Gligar (Guraiga)
208. Steelix (Haganeeru)
209. Snubbull
210. Granbull
211. Qwilfish (Hariisen)
212. Scizor (Hassamu)
213. Shuckle (Tsubotsubo)
214. Heracross
215. Sneasel (Nyuura)
216. Teddiursa (Himeguma)
217. Ursaring (Ringuma)
218. Slugma (Magumaggu)
219. Magcargo
220. Swinub (Urimuu)
221. Piloswine (Inomuu)
222. Corsola (Saniigo)
223. Remoraid (Teppouo)
224. Octillery (Okutan)
225. Delibird
226. Mantine
227. Skarmory (Eaamudo)
228. Houndour (Derubiru)
229. Houndoom (Herugaa)
230. Kingdra
231. Phanpy (Gomazou)
232. Donphan
233. Porygon2
234. Stantler (Odoshishi)
235. Smeargle (Douburu)
236. Tyrogue (Barukii)
237. Hitmontop (Kapoera)
238. Smoochum (Muchuuru)
239. Elekid
240. Magby (Bubi)
241. Miltank
242. Blissey (Hapinasu)
243. Raikou
244. Entei
245. Suicune
246. Larvitar (Yougirasu)
247. Pupitar (Sanagirasu)
248. Tyranitar (Bangirasu)
249. Lugia
250. Ho-Oh
251. Celebi

Pokémon Ruby/Sapphire added another 135 new Pokémon (as well as reusing 67 existing ones, which are marked with ¹ in the following list), but started a new numbering scheme. The Pokemon from these editions are:

1. Treeko (Kimori)
2. Grovyle (Juputoru)
3. Sceptile (Jukain)
4. Torchic (Achamo)
5. Combusken (Wakashamo)
6. Blaziken (Bashamo)
7. Mudkip (Mizugorou)
8. Marshtomp (Numakuroo)
9. Swampert (Raguraaji)
10. Poochyena (Pochiena)
11. Mightyena (Guraena)
12. Zigzagoon (Jiguzaguma)
13. Linoone (Massuguma)
14. Wurmple (Kemusso)
15. Silcoon (Karasarisu)
16. Beautifly (Agehanto)
17. Cascoon (Mayurudo)
18. Dustox (Dokukeiru)
19. Lotad (Hasuboo)
20. Lombre (Hasuburero)
21. Lodicolo (Runpappa)
22. Seedot (Taneboo)
23. Nuzleaf (Konohana)
24. Shiftry (Daatengu)
25. Taillow (Subame)
26. Swellow (Oosubame)
27. Wingull (Kyamome)
28. Pelipper (Peripaa)
29. Ralts (Rarutosu)
30. Kirlia (Kiruria)
31. Gardevoir (Saanaito)
32. Surskit (Ametama)
33. Masquerain (Amemoosu)
34. Shroomish (Kinokoko)
35. Breloom (Kinogassa)
36. Slakoth (Namakero)
37. Vigoroth (Yarukimono)
38. Slaking (Kekkingu)
39. Abra (Keishii)¹
40. Kadabra (Yungreaa)¹
41. Alakazam (Fudin)¹
42. Nincada (Tsuchinin)
43. Ninjask (Tekkanin)
44. Shedinja (Nukenin)
45. Whismer (Gonyonyo)
46. Loudred (Dogoomu)
47. Exploud (Bakuongu)
48. Makuhita (Makunoshita)
49. Hariyama (Hariteyama)
50. Goldeen (Tosakinto)¹
51. Seaking (Azumaou)¹
52. Magikarp (Koiking)¹
53. Gyarados (Gayarodosu)¹
54. Azurill (Ruriri)
55. Marill (Mariru)¹
56. Azumarill (Mairuri)¹
57. Geodude (Isitsubute)¹
58. Graveler (Gouron)¹
59. Golem (Gorounya)¹
60. Nosepass (Nozupasu)
61. Skitty (Eneko)
62. Delcatty (Enekororo)
63. Zubat (Zubatto)¹
64. Golbat (Gorubatto)¹
65. Crobat (Kurobattou)¹
66. Tentacool (Menokurage)¹
67. Tentacruel (Dokukurage)¹
68. Sableye (Yamirami)
69. Mawile (Kuchiito)
70. Aron (Kokodora)
71. Lairon (Kodora)
72. Aggron (Bosukodora)
73. Machop (Wanrikii)¹
74. Machoke (Gorikii)¹
75. Machamp (Kairikii)¹
76. Meditite (Asanan)
77. Medicham (Chaaremu)
78. Electrike (Rakurai)
79. Manectric (Raiboruto)
80. Plusle (Purasuru)
81. Minun (Mainan)
82. Magnemite (Koiru)¹
83. Magneton (Reakoiruu)¹
84. Voltorb (Biriridama)¹
85. Electrode (pokemon) (Marumain)¹
86. Volbeat (Barubiito)
87. Illumise (Irumiize)
88. Oddish (Nazunokusa)¹
89. Gloom (Kusaihana)¹
90. Vileplume (Rafureshiaa)¹
91. Bellossom (Kereihana)¹
92. Doduo (Douduo)¹
93. Dodrio (Doudariou)¹
94. Roselia (Rozeria)
95. Gulpin (Gokurin)
96. Swalot (Marunoomu)
97. Carvahna (Kibania)
98. Sharpedo (Samehadaa)
99. Wailmer (Hoeruko)
100. Wailord (Hoeruoo)
101. Numel (Donmeru)
102. Camerupt (Bakuuda)
103. Slugma (Magumaggu)¹
104. Magcargo (Magukarugo)¹
105. Torkoal (Kootasu)
106. Grimer (Betobetaa)¹
107. Muk (Betobeton)¹
108. Koffing (Dogaasu)¹
109. Weezing (Matadogasu)¹
110. Spoink (Banebuu)
111. Grumpig (Buupiggu)
112. Sandshrew (Sanddo)¹
113. Sandslash (Sandopan)¹
114. Spinda (Pacchiiru)
115. Skarmory (Eaamundo)¹
116. Trapinch (Nakkuraa)
117. Vibrava (Biburaaba)
118. Flygon (Furaigon)
119. Cacnea (Sabonea)
120. Cacturne (Nokutasu)
121. Swablu (Chirutto)
122. Altaria (Chirutarisu)
123. Zangoose (Zanguusu)
124. Seviper (Habuneeku)
125. Lunatone (Runatoon)
126. Solrock (Sorurokku)
127. Barboach (Dojocchi)
128. Whiscash (Namazun)
129. Corphish (Heigani)
130. Crawdaunt (Shizarigaa)
131. Baltoy (Yajiron)
132. Claydol (Nendooru)
133. Lileep (Ririira)
134. Cradily (Yureidoru)
135. Anorith (Anopusu)
136. Armaldo (Aamarudo)
137. Igglybuff (Pupurin)¹
138. Jigglypuff (Purin)¹
139. Wigglytuff (Pukurin)¹
140. Feebas (Hinbasu)
141. Milotic (Mirokarosu)
142. Castform (Powarun)
143. Staryu (Hitodemon)¹
144. Starmie (Satarumii)¹
145. Kelceon (Kakureon)
146. Shuppet (Kagebouzu)
147. Banette (Jupetta)
148. Duskull (Yomawaru)
149. Dusclops (Samayooru)
150. Tropius (Toropiusu)
151. Chimecho (Chiriin)
152. Absol (Abusoru)
153. Vulpix (Rokon)¹
154. Ninetales (Kyuukon)¹
155. Pichu (Piichu)¹
156. Pikachu (Pikachuu)¹
157. Raichu (Raichuu)¹
158. Psyduck (Kodakku)¹
159. Golduck (Goruddakku)¹
160. Wynaut (Soonano)
161. Wobbuffet (Soonasu)¹
162. Natu (Neitei)¹
163. Xatu (Neiteio)¹
164. Girafarig (Kirinriki)¹
165. Phanpy (Gomazou)¹
166. Donphan (Donfan)¹
167. Pinsir (Kairosu)¹
168. Heracross (Herakurosu)¹
169. Rhyhorn (Saihoun)¹
170. Rhydon (Saidon)¹
171. Snorunt (Yukiwarashi)
172. Glaile (Onigoori)
173. Spheal (Tamazarashi)
174. Sealeo (Todoguraa)
175. Walrein (Todozeruga)
176. Clamperl (Paaruru)
177. Huntail (Hanteeru)
178. Gorebyss (Sakurabisu)
179. Relicanth (Jiiransu)
180. Corsola (Saniigo)¹
181. Chinchou (Chonchii)¹
182. Lanturn (Rantaan)¹
183. Luvdisc (Rabukasu)
184. Horsea (Tattsuu)¹
185. Seadra (Shiidora)¹
186. Kingdra (Kingudora)¹
187. Bagon (Tatsubei)
188. Shelgon (Komoruu)
189. Salamence (Boomanda)
190. Beldum (Danbaru)
191. Metang (Metangu)
192. Metagross (Metagurosu)
193. Regirock (Rejirokku)
194. Regice (Rejiaisu)
195. Registeel (Rejisuchiru)
196. Latias (Ratiasu)
197. Latios (Ratiosu)
198. Kyogre (Kaiooga)
199. Groudon (Guraadon)
200. Rayquaza (Rekkuuza)
201. Jirachi (Jiraachi)
202. Deoxys (Deokishisu)

External links

• Pokemon Information

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "List of Pokémon."

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Natural number

(From Wikipedia, the free Encyclopedia)

A natural number is a non-negative integer: 0, 1, 2, 3, 4, ... (Zero is sometimes excluded.) These are the first numbers learned by children, and the easiest to understand. Natural numbers have two main purposes: they can be used for counting ("there are 3 apples on the table), or they can be used for ordering ("this is the 3rd largest city in the state"). The deeper properties of the natural numbers, such as the distribution of prime numbers, are studied in number theory.

History of natural numbers and the status of zero

Natural numbers were originally invented to count physical objects. Their first systematic study as things in themselves (separated from physical objects) is usually credited to the Greek philosophers Pythagoras and Archimedes. However, independent studies occurred at around the same time in India, China, and Mesoamerica.

Zero is relatively newborn. A zero digit was used in place-value notation as early as 400 BC by the Babylonians. The Olmec and Maya civilization used zero as a separate number as early as 1st century BC, apparently developed independently, but they did not pass it along to anyone outside of Mesoamerica. The modern concept dates to the Indian mathematician Brahmagupta in 628 AD. It took more than five centuries for European mathematicians to accept zero as a number, and even when they did, it was not counted as a natural number.

In the nineteenth century, a set-theoretical definition of the natural numbers was developed. With this definition, it was more convenient to include zero (corresponding to the empty set) in the naturals. Wikipedia follows this convention, as do set theorists, logicians, and computer scientists. Some other mathematicians, mainly number theorists, prefer to follow the old tradition and exclude zero from the natural numbers.

The term whole number is used informally by some authors for an element of the set of integers, the set of non-negative integers, or the set of positive integers.

Notation

Mathematicians use N or (an N in blackboard bold) to refer to the set of all natural numbers. This set is infinite but countable by definition.

W or is sometimes used to refer to the set of whole numbers, by authors who do not identify it with the integers.

Formal definitions

The precise mathematical definition of the natural numbers has not been easy. The Peano postulates state conditions that any successful definition must satisfy:

• There is a natural number 0.
• Every natural number a has a successor, denoted by a + 1.
• There is no natural number whose successor is 0.
• Distinct natural numbers have distinct successors: if a ≠ b, then a + 1 ≠ b + 1
• If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all natural numbers. (This postulate ensures that the proof technique of mathematical induction is valid.)

If zero is excluded from the natural numbers, every 0 in the Peano postulates should be replaced by a 1.

A standard construction in set theory is to define each natural number as the set of natural numbers less than it, so that 0 = {}, 1 = {0}, 2 = {0,1}, 3 = {0,1,2}... When you see a natural number used as a set, this is typically what is meant. Under this definition, there are exactly n elements in the set n and if m is bigger than n, then n is a subset of m.

Properties

One can inductively define an addition on the natural numbers by requiring a + 0 = a and a + (b + 1) = (a + b) + 1. This turns the natural numbers (N, +) into a commutative monoid with neutral element 0, the so-called free monoid with one generator. This monoid satisfies the cancellation property and can therefore be embedded in a group. The smallest group containing the natural numbers is the integers.

Analogously, a multiplication * can be defined via a * 0 = 0 and a * (b + 1) = ab + a. This turns (N, *) into a commutative monoid; addition and multiplication are compatible which is expressed in the distribution law: a * (b + c) = ab + ac.

Furthermore, one defines a total order on the natural numbers by writing a ≤ b if and only if there exists another natural number c with a + c = b. This order is compatible with the arithmetical operations in the following sense: if a, b and c are natural numbers and a <= b, then a + c ≤ b + c and ac ≤ bc. An important property of the natural numbers is that they are well-ordered: every non-empty set of natural numbers has a smallest element.

While it is in general not possible to divide one natural number by another and get a natural number as result, the procedure of division with remainder is available as a substitute: For any two natural numbers a and b with b ≠ 0 we can find natural numbers q and r such that

a = bq + r and r < b

The number q is called the quotient and r is called the remainder of division of a by b. The numbers q and r are uniquely determined by a and b. This, the quotient-remainder theorem, is key to several other properties (divisibility), algorithms (such as the Euclidean algorithm), and ideas in number theory.

Generalizations

Two generalizations of natural numbers arise from the two uses: ordinal numbers are used to describe the position of an element in a ordered sequence and cardinal numbers are used to specify the size of a given set.

For finite sequences or finite sets, both of these are of course the same as the natural numbers.
zh-cn:自然数 zh-tw:自然數

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Natural number."

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Number

(From Wikipedia, the free Encyclopedia)

simple:Number

A number is an abstract entity used to describe quantity. There are different types of numbers. The most familiar numbers are the natural numbers {0, 1, 2, ...} used for counting and denoted by N. If the negative whole numbers are included, one obtains the integers Z. Ratios of integers are called rational numbers or fractions; the set of all rational numbers is denoted by Q. If all infinite and non-repeating decimal expansions are included, one obtains the real numbers R. Those real numbers which are not rational are called irrational numbers. The real numbers are in turn extended to the complex numbers C in order to be able to solve all algebraic equations. The above symbols are often written in blackboard bold, thus:

Numbers should be distinguished from numerals which are symbols used to represent numbers. The notation of numbers as series of digits is discussed in numeral systems.

People like to assign numbers to objects in order to have unique names. There are various numbering schemes for doing so.

Extensions

Newer developments are the hyperreal numbers and the surreal numbers which extend the real numbers by adding infinitesimal and infinitely large numbers. While (most) real numbers have infinitely long expansions to the right of the decimal point, one can also try to allow for infinitely long expansions to the left, leading to the p-adic numbers. For dealing with infinite collections , the natural numbers have been generalized to the ordinal numbers and to the cardinal numbers. The former give the ordering of the collection, the latter its size. (For the finite case, the ordinal and cardinal numbers are equivalent; they diverge in the infinite case.)

The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra; one obtains the groupss, ringss and fields.

Particular numbers

See: List of numbers, mathematical constants, even and odd numbers, negative and non-negative numbers, small numbers, large numbers, orders of magnitude (numbers)

See also

• Numbers in various languages

External links

• Wiktionary article on number
• What's special about this number?

  Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Number."

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Numbers

(From Wikipedia, the free Encyclopedia)

• Number
• Book_of_Numbers

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Numbers."

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Palindromic number

(From Wikipedia, the free Encyclopedia)

A palindromic number is a symmetrical number written in some base a as a₁a₂a₃ ...|... a₃a₂a₁.

All numbers in base 10 with one digit {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} are palindromic ones. The number of palindromic numbers with two digits is 9:

{11, 22, 33, 44, 55, 66, 77, 88, 99}.

There are 90 palindromic numbers with three digits:

{101, 111, 121, 131, 141, 151, 161, 171, 181, 191, ..., 909, 919, 929, 939, 949, 959, 969, 979, 989, 999}

and also 90 palindromic numbers with four digits:

{1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, ..., 9009, 9119, 9229, 9339, 9449, 9559, 9669, 9779, 9889, 9999},

so there are 199 palindromic numbers below 10⁴. Below 10⁵ there are 1099 palindromic numbers and for other exponents of 10ⁿ we have: 1999,10999,19999,109999,199999,1099999, ... (SIDN A070199). For some types of palindromic numbers these values are listed below in a table. Here 0 is included.

	101	102	103	104	105	106	107	108	109	1010
n natural	9	90		199	1099	1999	10999	19999	109999	199999
n even	5	9	49	89	489	+	+	+	+	+
n odd	5	10	60	110	610	+	+	+	+	+
n perfect square	3		6		13	14	19		+	+
n prime	4	5	20		113		781		5953
n square-free	6	12	67	120	675	+	+	+	+	+
n non-square-free (μ(n)=0)	3	6	41	78	423	+	+	+	+	+
n square with prime root	2		3		5
n with an even number of distinct prime factors (μ(n)=1)	2	6	35	56	324	+	+	+	+	+
n with an odd number of distinct prime factors (μ(n)=-1)	5	7	33	65	352	+	+	+	+	+
n even with an odd number of prime factors
n even with ann odd number of distinct prime factors	1	2	9	21	100	+	+	+	+	+
n odd with an odd number of prime factors	0	1	12	37	204	+	+	+	+	+
n odd with an odd number of distinct prime factors	0	0	4	24	139	+	+	+	+	+
n even squarefree with an even number of distinct prime factors	1	2	11	15	98	+	+	+	+	+
n odd squarefree with an even number of distinct prime factors	1	4	24	41	226	+	+	+	+	+
n odd with exactly 2 prime factors	1	4	25	39	205	+	+	+	+	+
n even with exactly 2 prime factors	2	3	11		64	+	+	+	+	+
n even with exactly 3 prime factors	1	3	14	24	122	+	+	+	+	+
n even with exactly 3 distinct prime factors
n odd with exactly 3 prime factors	0	1	12	34	173	+	+	+	+	+
n Carmichael number	0	0	0	0	0	1+	+	+	+	+
n for which σ(n) is palindromic	6	10	47	114	688	+	+	+	+	+
add more

Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Palindromic number."

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Abbreviations & Acronyms: Number

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Modern Usage: Number

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Commercial Usage: Number

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Image Slideshow: Number

Photos: Number More pictures...

Illustrations: Number More pictures...

Computer Images: Number More pictures...

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Photo Album: Number

Thumbnail	Description & Credit	Thumbnail	Description & Credit
	Shown is an ad from the Washington Post November 6, 1985. The ad talks about fats, vegetables, Vitamin A and C, and fiber. It states the fiber or roughage may help prevent colon cancer. It also shows the 1-800-4-CANCER phone number. Credit: Unknown photographer/artist.		This is a histological slide stained with H&E of a human herpesvirus (HHV-6), a type of human herpes virus. In this photomicrograph of infected cells, the black specks indicate the location of a radioactive isotope that has been attached to the viral RNA. In this case, a large number of black specks indicate that this lymphocyte has been infected. Credit: Unknown photographer/artist.
	In the early 1950's, there were more than 20,000 cases of polio each year. After polio vaccination began in 1955, cases dropped significantly. By 1960, the number of cases dropped to about 3,000, and by 1979 there were only about 10. Credit: CDC.		Bar graph showing increasing number of office visits for treatment of middle ear infections. Credit: CDC.
	"2D Cross Section of a 5-Brane" (movie) by Bob Rutkiewicz. From Physics String Theory/M-Theory, a 5-brane equation that has the same number of holes as the full 10-brane. Use DPGraph's Scrollbar to vary A or B.		Unusual number of islets to chart. Credit: Coast & Geodetic Survey Historical Image Collection.
	The Gulf Stream by the Coast Survey Based on a series of studies beginning in 1845 The Coast Survey established a number of sections for repeated observations The first systematic oceanographic studies of the Gulf Stream Integrated oceanography, marine geology, and meteorology into these cruises. Credit: Coast & Geodetic Survey Historical Image Collection.		Washington Monument and Smithsonian Institution as seen from Potomac River. In: "Protection from Lightning" by Alexander McAdie. 1894. Library Call Number TH 9057.M3 1894. Credit: America's Coastlines.
	"View of Benicia from the West", frontispiece. In: Reports of Explorations and Surveys .... Vol. 5. Commonly known as Pacific Railroad Surveys. Call Number F593 .U58. Credit: America's Coastlines.		"The Emperors' Conclave". In: "The Heart of the Antarctic", Volume II, by E. H. Shackleton, 1909. P. 240. Library Call Number G149 S52. Credit: Paths Less Taken - NOAA at the Ends of the Earth.
Source: pictures compiled by the editor from various references; see picture credits.

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Digital Photo Gallery: Number
 

"True Story Number One" by Kelly Abbott Commentary: "They don't sell Nikes."	"Cellphone number pad" by Julia Eisenberg Commentary: "Cellphone number pad."
Source: photographs selected by the editor, with permission from the photographers.

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Sounds Captioned with "Number".

Play	Caption	Play	Caption
	Dialing a telephone number from a rotary dial telephone.		Dialing a telephone number from a rotary dial telephone.
Source: compiled by the editor from various references; see credits.

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Familiar Quotations: Number

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Historic Usage: Number

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Use in Literature: Number