Title	Order of Merit
Awarded by	the
Type	Dynastic order
Motto	''FOR MERIT''
Eligibility	All living citizens of the Commonwealth realms
For	At the monarch's pleasure
Status	Currently constituted
Head title	Sovereign
Head	Elizabeth II
House	House of Windsor
Grades	Member (OM)
Date	1902
First induction	Frederick Roberts, 1st Earl Roberts 26 June 1902
Higher	Dependent on state
Lower	Dependent on state
Image2
Caption2	Ribbon of the Order of Merit }}

The Order of Merit () is a dynastic order recognising distinguished service in the armed forces, science, art, literature, or for the promotion of culture. Established in 1902 by King Edward VII, admission into the order remains the personal gift of its Sovereign, the reigning monarch of the Commonwealth realms, and is limited to 24 living recipients at one time from these countries plus a limited number of honorary members. While all members receive the ability to use the post-nominal letters ''OM'' and a medallion for life, the Order of Merit's precedence amongst other honours differs amongst Commonwealth realms.

History

The first mention of a possible Order of Merit was made following the Battle of Trafalgar in 1805, in correspondence between First Lord of the Admiralty Lord Barham and William Pitt, though nothing eventuated from the idea. Later, it was thought by Queen Victoria, her courtiers, and politicians alike, that a new order, based on the Prussian order ''Pour le Mérite'', would make up for the insufficient recognition offered by the established honours system to achievement outside of public service, in realms such as art, music, literature, industry, and science. Victoria's husband, Albert, Prince Consort, took an interest in the matter; it was recorded in his diary that he met on 16 January 1844 with Robert Peel to discuss the "idea of institution of a civil Order of Merit" and three days later he conferred with the Queen on the subject. The concept did not wither and, on 5 January 1888, British prime minister Lord Salisbury submitted to the Queen a draft constitution for an Order of Merit in Science and Art, consisting of one grade split into two branches of knighthood: the Order of Scientific Merit for Knights of Merit in Science, with the post-nominal letters ''KMS'' and the Order of Artistic Merit for Knights of Merit in Art, with the post-nominal letters ''KMA''. However, Sir Frederic Leighton, President of the Royal Academy, advised against the new order, primarily because of its selection process.

It was Victoria's son, Edward VII, who eventually founded the Order of Merit on 26 June 1902 the date for which his coronation had been originally planned as a means to acknowledge "exceptionally meritorious service in Our Navy and Our Army, or who may have rendered exceptionally meritorious service towards the advancement of Art, Literature and Science"; all modern aspects of the order were established under his direction, including the division for military figures. From the outset, prime ministers attempted to propose candidates or lobbied to influence the monarch's decision on appointments, but the Royal Household adamantly guarded information about potential names. After 1931, when the Statute of Westminster came into being and the Dominions of the British Empire became independent states, equal in status to the UK, the Order of Merit remained an honour open to all the King's realms; thus, as with the monarch who conferred it, the order ceased to be purely British.

From its inception, the order has been open to women, Florence Nightingale being the first woman to receive the honour, in 1907. Several individuals have refused admission into the Order of Merit, such as Rudyard Kipling, A. E. Housman, and George Bernard Shaw. To date, Prince Philip, Duke of Edinburgh, remains the youngest person ever inducted into the Order of Merit, having been admitted by Queen Elizabeth II in 1968, when he was 47 years of age.

Eligibility and appointment

All citizens of the Commonwealth realms are eligible for appointment to the Order of Merit. There may be, however, only 24 living individuals in the order at any given time, not including honorary appointees, and new members are personally selected by the reigning monarch of the 16 realms, presently Queen Elizabeth II, with the assistance of her private secretaries; the order has thus been described as "quite possibly, the most prestigious honour one can receive on planet Earth." Within the limited membership is a designated military division, with its own unique insignia; though it has not been abolished, it is currently unpopulated, Lord Mountbatten of Burma having been the last person so honoured. Honorary members form another group, to which there is no numerical limit, though such appointments are rare; individuals from countries in the Commonwealth of Nations that are not headed by Elizabeth II are therefore considered foreigners, and thus are granted only honorary admissions, such as Nelson Mandela (South Africa) and Mother Teresa (India).

Upon admission into the Order of Merit, members are entitled to use the post-nominal letters ''OM'', and are entrusted with the badge of the order, consisting of a golden crown from which is suspended a red enamelled cross, itself centred by a disk of blue enamel, surrounded by a gold laurel wreath, and bearing in gold lettering the words ''FOR MERIT''; the insignia for the military grouping is distinguished by a pair of crossed swords behind the central disk. The ribbon of the Order of Merit is divided into two stripes of red and blue; men wear their badges on a neck ribbon, while women carry theirs on a ribbon bow pinned to the left shoulder, and aides-de-camp may wear the insignia on their aiguillettes. Since 1991, it has been required that the insignia be returned upon the recipient's death.

Current members

Sovereign: Queen Elizabeth II

Members:

Image:Flag of EIIR.svgPrince consortOwen ChadwickAndrew HuxleyFrederick Sanger OM Order of the Companions of HonourMargaret ThatcherMichael AtiyahAaron KlugNorman Foster, Baron Foster of Thames BankAnthony CaroRoger PenroseTom StoppardImage:Flag of EIIR.svgRobert May, Baron May of OxfordJacob Rothschild, 4th Baron RothschildDavid AttenboroughBetty BoothroydMichael Howard (historian)Robin EamesTim Berners-LeeMartin Rees, Baron Rees of LudlowJean ChrétienPrivy Council of CanadaNeil MacGregor OMDavid Hockney OM CHJohn Howard OM AC Star of the Solomon Islands

Member Number !! Name !! Known for !! Date of appointment !! Age
1-(122)	23px The Duke of Edinburgh KG KT OM GBE QSO AC GCL PC	royal consort ||	10 June 1968
2-(145)	The Reverend Owen Chadwick OM KBE ||	Theology>theological historian	11 November 1983
3-(146)	Sir Andrew Huxley OM|| physiologist, Nobel laureate, and former President of the Royal Society ||	11 November 1983
4-(151)	CH CBE ||	Biochemistry>biochemist and double Nobel laureate	11 February 1986
5-(158)	The Baroness Thatcher LG OM PC ||	former Prime Minister of the United Kingdom	7 December 1990
6-(162)	Sir Michael Atiyah OM || mathematician, Fields Medalist, Abel laureate, and former President of the Royal Society ||	17 November 1992
7-(166)	Sir Aaron Klug OM||	Biophysics>biophysicist, Nobel laureate, and former President of the Royal Society	23 October 1995
8-(169)	The Lord Foster of Thames Bank OM|| architect and Pritzker laureate ||	25 November 1997
9-(174)	Sir Anthony Caro OM CBE||	Sculpture>sculptor	9 May 2000
10-(175)	Sir Roger Penrose OM ||	Penrose tiling>mathematical physicist	9 May 2000
11-(176)	Sir Tom Stoppard OM CBE||	playwright	9 May 2000
12-(177)	23px The Prince of Wales KG KT GCB OM AK QSO SOM CD||	Conservation movement>conservationist	27 June 2002
13-(178)	The Lord May of Oxford OM AC ||	Ecology>ecologist and former President of the Royal Society	28 October 2002
14-(179)	The Lord Rothschild OM GBE ||	Philanthropy>philanthropist	28 October 2002
15-(180)	Sir David Attenborough OM CH CVO CBE ||	presenter>broadcaster	10 June 2005
16-(181)	The Lady Boothroyd OM PC ||	Speaker of the House of Commons (United Kingdom)>Speaker of the United Kingdom House of Commons	10 June 2005
17-(182)	Sir Michael Howard OM CH CBE MC ||	military historian	10 June 2005
18-(183)	The Lord Eames OM || Primate of All Ireland and Archbishop of Armagh ||	13 June 2007
19-(184)	Sir Tim Berners-Lee OM KBE ||	inventor of the World Wide Web and Director of the World Wide Web Consortium	13 June 2007
20-(185)	The Lord Rees of Ludlow OM ||	Astronomer Royal and former President of the Royal Society	13 June 2007
21-(186)	PC OM CC QC ||	former Prime Minister of Canada	13 July 2009
22-(187)	| art historian and Director of the British Museum ||	4 November 2010
23-(188)	|	artist	1 January 2012
24-(189)	SSI ||	former Prime Minister of Australia	1 January 2012

Honorary members

(165) Nelson Mandela, statesman and Nobel laureate, appointed 21 March 1995

Precedence in each realm

As the Order of Merit is open to the citizens of sixteen different countries, each with their own system of orders, decorations, and medals, the order's place of precedence varies from country to country. While, in the United Kingdom, the order's postnominal letters follow those of Knights and Dames Grand Cross of the Order of the Bath, membership in the Order of Merit itself gives members no place in any of the orders of precedence in the United Kingdom. However, it has been claimed by Stanley Martin, in his book ''The Order of Merit 1902-2002: One Hundred Years of Matchless Honour'', that the Order of Merit is actually the pinnacle of the British honours system. Similarly, though it was not listed in the Canadian order of precedence for honours, decorations, and medals until December 2010, except relating to those who were appointed to the order prior to 1 June 1972,. Christopher McCreery, an expert on Canadian honours and secretary to the Lieutenant Governor of Nova Scotia, stated that the Order of Merit was the highest civilian award for merit a Canadian could receive.

Some orders of precedence are as follows:

align="center"Order of the BathCross of Valour (Canada)Order of the Bath

colspan="2" align="center"	Country	Preceding	>align="center"| Following
colspan="2" bgcolor="#A9A9A9"	<	AustraliaOrder of precedence	Knight/Dame Grand Cross of the Most Honourable Order of the Bath (GCB) || Knight/Dame of the Order of Australia (AK/AD)
colspan="2" bgcolor="#A9A9A9"> '''CanadaCanadian order of precedence (decorations and medals)	Order of precedence	Cross of Valour (CV) || Companion of the Order of Canada (CC)
colspan="2" bgcolor="#A9A9A9"	New ZealandOrder of precedence	Knight/Dame Grand Cross of the Most Honourable Order of the Bath (GCB) || Member of the Order of New Zealand (ONZ)

Past members

Substantive members

Countries///////

	|	Name	Date of appointment	Date of death
1.	|	Frederick Roberts, 1st Earl Roberts>The Earl Roberts	26 June 1902	14 November 1914
2.	|	Garnet Wolseley, 1st Viscount Wolseley>The Viscount Wolseley	26 June 1902	25 March 1913
3.	|	Herbert Kitchener, 1st Earl Kitchener>The Lord Kitchener of Khartoum	26 June 1902	5 June 1916
4.	|	John Strutt, 3rd Baron Rayleigh>The Lord Rayleigh	26 June 1902	30 June 1919
5.	|	William Thomson, 1st Baron Kelvin>The Lord Kelvin	26 June 1902	17 December 1907
6.	|	Joseph Lister, 1st Baron Lister>The Lord Lister	26 June 1902	10 February 1912
7.	|	Henry Keppel>Sir Henry Keppel	26 June 1902	17 January 1904
8.	|	John Morley, 1st Viscount Morley of Blackburn>John Morley	26 June 1902	23 September 1923
9.	|	William Edward Hartpole Lecky	26 June 1902	22 October 1903
10.	|	Edward Hobart Seymour>Sir Edward Hobart Seymour	26 June 1902	2 March 1929
11.	|	William Huggins>Sir William Huggins	26 June 1902	12 May 1910
12.	|	George Frederic Watts	26 June 1902	1 July 1904
13.	|	George White (British Army officer)>Sir George Stuart White	30 June 1905	24 June 1912
14.	|	John Fisher, 1st Baron Fisher>Sir John Fisher	30 June 1905	10 July 1920
15.	|	Richard Claverhouse Jebb>Sir Richard Claverhouse Jebb	30 June 1905	9 December 1905
16.	|	Lawrence Alma-Tadema>Sir Lawrence Alma-Tadema	30 June 1905	25 June 1912
17.	|	George Meredith	30 June 1905	18 May 1909
18.	|	William Holman Hunt	30 June 1905	7 September 1910
22.	|	Evelyn Baring, 1st Earl of Cromer>The Earl of Cromer	29 June 1906	29 January 1917
23.	|	James Bryce, 1st Viscount Bryce>James Bryce	11 February 1907	22 January 1922
24.	|	Joseph Dalton Hooker>Sir Joseph Dalton Hooker	30 June 1907	10 December 1911
25.	|	Florence Nightingale	12 May 1907	13 August 1910
26.	|	Henry Jackson (classicist)>Henry Jackson	26 June 1908	25 September 1921
27.	|	Alfred Russel Wallace	26 June 1908	7 November 1913
28.	|	William Crookes>Sir William Crookes	8 July 1910	4 April 1919
29.	|	Thomas Hardy	8 July 1910	11 January 1928
30.	|	Sir George Trevelyan, 2nd Baronet>Sir George Trevelyan, Bt	19 June 1911	17 August 1928
31.	|	Edward Elgar>Sir Edward Elgar, Bt	19 June 1911	23 February 1934
32.	|	Arthur Wilson (Royal Navy officer)>Sir Arthur Wilson	8 March 1912	25 May 1921
33.	|	J. J. Thomson>Sir J. J. Thomson	15 March 1912	30 August 1940
34.	|	Archibald Geikie>Sir Archibald Geikie	1 January 1914	10 November 1924
35.	|	John French, 1st Earl of Ypres>Sir John French	3 December 1914	22 May 1925
36.	|	Richard Haldane, 1st Viscount Haldane>The Viscount Haldane	26 May 1915	19 August 1928
37.	|	Henry James	1 January 1916	28 February 1916
38.	|	John Jellicoe, 1st Earl Jellicoe>Sir John Jellicoe	31 May 1916	20 November 1935
39.	|	Arthur Balfour	3 June 1916	19 March 1930
41.	|	David Beatty, 1st Earl Beatty>Sir David Beatty	3 June 1919	11 March 1936
42.	|	Douglas Haig, 1st Earl Haig>Douglas Haig	3 June 1919	29 January 1928
44.	|	David Lloyd George	5 August 1919	26 March 1945
45.	|	J. M. Barrie>Sir J. M. Barrie, Bt	2 January 1922	19 June 1937
46.	|	F. H. Bradley	3 June 1924	18 September 1924
47.	|	Charles Scott Sherrington>Sir Charles Scott Sherrington	3 June 1924	4 March 1952
48.	|	James George Frazer>Sir James George Frazer	1 January 1925	7 May 1941
49.	|	Ernest Rutherford	1 January 1925	19 October 1937
50.	|	Charles Algernon Parsons>Sir Charles Algernon Parsons	3 June 1927	11 February 1931
51.	|	George Abraham Grierson>Sir George Abraham Grierson	4 June 1928	9 March 1941
52.	|	Robert Bridges>Robert Seymour Bridges	3 June 1929	21 April 1930
53.	|	John Galsworthy	3 June 1929	31 January 1933
54.	|	Samuel Alexander	3 June 1930	13 September 1938
55.	|	M. R. James	3 June 1930	12 June 1936
56.	|	G. M. Trevelyan	3 June 1930	21 July 1962
57.	|	Sir Charles Madden, 1st Baronet>Sir Charles Madden, Bt	1 January 1931	5 June 1935
58.	|	Philip Wilson Steer	1 January 1931	18 March 1942
59.	|	William Henry Bragg>Sir William Henry Bragg	3 June 1931	10 March 1942
60.	|	John William Mackail	1 January 1935	13 December 1945
61.	|	John Masefield>John Edward Masefield	3 June 1935	12 May 1967
62.	|	Ralph Vaughan Williams	3 June 1935	26 August 1958
63.	|	Frederick Gowland Hopkins>Sir Frederick Gowland Hopkins	3 June 1935	16 May 1947
64.	|	Philip Chetwode, 1st Baron Chetwode>Sir Philip Chetwode, Bt	1 January 1936	6 July 1950
65.	|	Herbert Fisher	1 February 1937	18 April 1940
66.	|	Robert Baden-Powell, 1st Baron Baden-Powell>The Lord Baden-Powell	11 May 1937	8 January 1941
67.	|	Arthur Eddington>Sir Arthur Eddington	9 June 1938	22 November 1944
68.	|	Ernle Chatfield, 1st Baron Chatfield>The Lord Chatfield	2 January 1939	15 November 1967
69.	|	James Hopwood Jeans>Sir James Hopwood Jeans	2 January 1939	16 September 1946
70.	|	Cyril Newall, 1st Baron Newall>Sir Cyril Newall	29 October 1940	30 November 1963
71.	|	Gilbert Murray	1 January 1941	20 May 1957
72.	|	Edwin Lutyens>Sir Edwin Lutyens	1 January 1942	1 January 1944
73.	|	Augustus John	11 June 1942	31 October 1961
74.	|	Edgar Adrian, 1st Baron Adrian>Edgar Adrian	11 June 1942	4 August 1977
75.	|	William Searle Holdsworth>Sir William Searle Holdsworth	1 January 1943	2 January 1944
76.	|	Dudley Pound>Sir Dudley Pound	3 September 1943	21 October 1943
77.	|	Sidney Webb, 1st Baron Passfield>The Lord Passfield	8 June 1944	13 October 1947
78.	|	Henry Hallett Dale>Sir Henry Hallett Dale	8 June 1944	23 July 1968
79.	|	Giles Gilbert Scott>Sir Giles Gilbert Scott	8 June 1944	8 February 1960
80.	|	Alfred North Whitehead	1 January 1945	30 December 1947
82.	|	Winston Churchill	1 January 1946	24 January 1965
83.	|	Charles Portal, 1st Viscount Portal of Hungerford>The Viscount Portal of Hungerford	1 January 1946	22 April 1971
84.	|	Alan Brooke, 1st Viscount Alanbrooke>The Viscount Alanbrooke	13 June 1946	17 June 1963
85.	|	Andrew Cunningham, 1st Viscount Cunningham of Hyndhope>The Viscount Cunningham of Hyndhope	13 June 1946	12 June 1963
86.	|	E. F. L. Wood, 1st Earl of Halifax>The Earl of Halifax	13 June 1946	23 December 1959
87.	|	Jan Smuts	1 January 1947	11 September 1950
89.	|	William Lyon Mackenzie King	17 November 1947	22 July 1950
90.	|	T. S. Eliot	1 January 1948	4 January 1965
91.	|	Robert Robinson (organic chemist)>Sir Robert Robinson	9 June 1949	8 February 1975
92.	|	Bertrand Russell>The Earl Russell	9 June 1949	2 February 1970
93.	|	Alexander Cadogan>Sir Alexander Cadogan	1 January 1951	9 July 1968
94.	|	Hugh Trenchard, 1st Viscount Trenchard>The Viscount Trenchard	1 January 1951	10 February 1956
95.	|	G. E. Moore	7 June 1951	24 October 1958
96.	|	Clement Attlee	5 November 1951	8 October 1967
97.	|	Wilder Penfield	1 January 1953	5 April 1976
98.	|	Walter de la Mare	1 June 1953	22 June 1956
100.	|	Malcolm Hailey, 1st Baron Hailey>The Lord Hailey	31 May 1956	1 June 1969
101.	|	John Cockcroft>Sir John Cockcroft	1 January 1957	18 September 1967
102.	|	John Anderson, 1st Viscount Waverley>The Viscount Waverley	8 December 1957	4 January 1958
103.	|	Frank Macfarlane Burnet>Sir Frank Macfarlane Burnet	12 June 1958	31 August 1985
104.	|	Herbert Samuel, 1st Viscount Samuel>The Viscount Samuel	21 November 1958	2 February 1963
105.	|	Harold Alexander, 1st Earl Alexander of Tunis>The Earl Alexander of Tunis	23 April 1960	16 June 1969
106.	|	Cyril Norman Hinshelwood>Sir Cyril Norman Hinshelwood	23 April 1960	9 October 1967
107.	|	Graham Sutherland	23 April 1960	17 February 1980
108.	|	Geoffrey de Havilland>Sir Geoffrey de Havilland	23 November 1962	21 May 1965
109.	|	Basil Spence>Sir Basil Spence	23 November 1962	19 November 1976
110.	|	Owen Dixon>Sir Owen Dixon	29 May 1963	7 July 1972
112.	|	George Peabody Gooch	16 August 1963	31 August 1968
113.	|	Henry Moore	16 August 1963	31 August 1986
114.	|	Benjamin Britten	23 March 1965	4 December 1976
115.	|	Dorothy Hodgkin	23 March 1965	29 July 1994
116.	|	Louis Mountbatten, 1st Earl Mountbatten of Burma>The Earl Mountbatten of Burma	15 July 1965	27 August 1979
117.	|	Howard Florey>The Lord Florey	15 July 1965	21 February 1968
118.	|	Patrick Blackett, Baron Blackett>Patrick Blackett	20 November 1967	13 July 1974
119.	|	William Walton>Sir William Walton	20 November 1967	8 March 1983
120.	|	Ben Nicholson	23 April 1968	6 February 1982
121.	|	Solly Zuckerman, Baron Zuckerman>Sir Solly Zuckerman	23 April 1968	1 April 1993
123.	|	E. M. Forster	1 January 1969	7 June 1970
124.	|	Malcolm MacDonald	14 July 1969	11 January 1981
125.	|	William Penney, Baron Penney>The Lord Penney	14 July 1969	3 March 1991
126.	|	Geoffrey Ingram Taylor>Sir Geoffrey Ingram Taylor	14 July 1969	27 June 1975
127.	|	Veronica Wedgwood>Dame Veronica Wedgwood	14 July 1969	9 March 1997
128.	|	John Cawte Beaglehole	21 March 1970	10 October 1971
129.	|	Lester B. Pearson	20 May 1971	27 December 1972
130.	|	Isaiah Berlin>Sir Isaiah Berlin	20 May 1971	5 November 1997
131.	|	George Edwards (aviation)>Sir George Edwards	20 May 1971	2 March 2003
132.	|	Alan Lloyd Hodgkin>Sir Alan Lloyd Hodgkin	17 April 1973	20 December 1998
133.	|	Paul Dirac	17 April 1973	20 October 1984
134.	|	Harold Macmillan	2 April 1976	29 December 1986
135.	|	Christopher Hinton, Baron Hinton of Bankside>The Lord Hinton of Bankside	2 April 1976	22 June 1983
136.	|	Kenneth Clark>The Lord Clark	2 April 1976	21 May 1983
137.	|	Ronald Syme>Sir Ronald Syme	2 April 1976	4 September 1989
138.	|	Alexander R. Todd, Baron Todd>The Lord Todd	24 October 1977	10 January 1997
139.	|	Oliver Franks, Baron Franks>The Lord Franks	24 October 1977	15 October 1992
140.	|	Frederick Ashton>Sir Frederick Ashton	24 October 1977	18 October 1988
141.	|	J. B. Priestley	24 October 1977	14 August 1984
142.	|	Laurence Olivier>The Lord Olivier	6 February 1981	11 July 1989
143.	|	Peter Medawar>Sir Peter Medawar	6 February 1981	2 October 1987
144.	|	Leonard Cheshire	6 February 1981	31 July 1992
147.	|	Sidney Nolan>Sir Sidney Nolan	11 November 1983	28 November 1992
148.	|	Michael Tippett>Sir Michael Tippett	11 November 1983	8 January 1998
150.	|	Graham Greene	11 February 1986	3 April 1991
152.	|	Frank Whittle>Sir Frank Whittle	11 February 1986	9 August 1996
153.	|	Yehudi Menuhin>Sir Yehudi Menuhin	25 February 1987	12 March 1999
154.	|	Ernst Gombrich>Sir Ernst Gombrich	15 February 1988	3 November 2001
155.	|	Max Perutz	15 February 1988	6 February 2002
156.	|	Cicely Saunders>Dame Cicely Saunders	30 November 1989	14 July 2005
157.	|	George Porter>Sir George Porter	30 November 1989	31 August 2002
159.	|	Joan Sutherland>Dame Joan Sutherland	29 November 1991	10 October 2010
160.	|	Francis Crick	27 November 1991	28 July 2004
161.	|	Ninette de Valois>Dame Ninette de Valois	17 November 1992	8 March 2001
163.	|	Roy Jenkins>The Lord Jenkins of Hillhead	6 December 1993	5 January 2003
164.	|	Lucian Freud	6 December 1993	20 July 2011
167.	|	John Gielgud>Sir John Gielgud	9 December 1996	21 May 2000
168.	|	Alfred Denning, Baron Denning>The Lord Denning	25 November 1997	5 March 1999
170.	|	Denis Rooke>Sir Denis Rooke	25 November 1997	2 September 2008
171.	|	Ted Hughes	10 August 1998	28 October 1998
172.	|	Basil Hume	25 May 1999	17 June 1999
173.	|	James W. Black>Sir James W. Black	9 May 2000	22 March 2010

Honorary members

Countries/

	|	Name	Date of appointment	Date of death
19.	|	Yamagata Aritomo>Prince Yamagata Aritomo	21 February 1906	1 February 1922
20.	|	Ōyama Iwao>Prince Ōyama Iwao	21 February 1906	10 December 1916
21.	|	Tōgō Heihachirō>Marquess Tōgō Heihachirō	21 February 1906	30 May 1934
40.	|	Ferdinand Foch	29 November 1918	20 March 1929
43.	|	Joseph Joffre	26 June 1919	3 January 1931
81.	|	Dwight D. Eisenhower	12 June 1945	28 March 1969
88.	|	John Gilbert Winant	1 January 1947	3 November 1947
99.	|	Albert Schweitzer	25 February 1955	4 September 1965
111.	|	Sarvepalli Radhakrishnan>Sir Sarvepalli Radhakrishnan	12 June 1963	17 April 1975
149.	|	Mother Teresa>Agnesë Gonxhe Bojaxhiu (Mother Teresa)	18 November 1983	5 September 1997

Notes

Citations

References

Category:Civil awards and decorations of Canada Category:Civil awards and decorations of the United Kingdom Category:Awards established in 1902

ca:Orde del Mèrit (Regne Unit) cs:Řád Za zásluhy (Velká Británie) da:Fortjenstordenen (Commonwealth of Nations) de:Order of Merit es:Orden de Mérito del Reino Unido eo:Brita Merit-Ordeno fr:Ordre du Mérite (Royaume-Uni) id:Order of Merit it:Ordine al Merito del Regno Unito he:מסדר ההצטיינות nl:Order of Merit (Verenigd Koninkrijk) ja:メリット勲章 no:Order of Merit pl:Order of Merit pt:Ordem de Mérito (Reino Unido) ru:Орден Заслуг (Великобритания) simple:Order of Merit fi:Ansioritarikunta sv:Order of Merit tr:Liyakat Nişanı (İngiltere) uk:Орден Заслуг (Велика Британія) zh:功績勳章

In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (''i.e.,'' in their processing time or working space requirements) to changes in input size.

Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation. A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols ''o'', Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates.

Big O notation is also used in many other fields to provide similar estimates.

Formal definition

Let ''f''(''x'') and ''g''(''x'') be two functions defined on some subset of the real numbers. One writes

:$f(x)=O(g(x))\backslash mbox\{\; as\; \}x\backslash to\backslash infty\backslash ,$

if and only if there is a positive constant M such that for all sufficiently large values of ''x'', ''f''(''x'') is at most M multiplied by ''g''(''x'') in absolute value. That is, ''f''(''x'') = ''O''(''g''(''x'')) if and only if there exists a positive real number ''M'' and a real number ''x''₀ such that

:$|f(x)|\; \backslash le\; \backslash ;\; M\; |g(x)|\backslash mbox\{\; for\; all\; \}x>x\_0.$

In many contexts, the assumption that we are interested in the growth rate as the variable ''x'' goes to infinity is left unstated, and one writes more simply that ''f''(''x'') = ''O''(''g''(''x'')). The notation can also be used to describe the behavior of ''f'' near some real number ''a'' (often, ''a'' = 0): we say

:$f(x)=O(g(x))\backslash mbox\{\; as\; \}x\backslash to\; a\backslash ,$

if and only if there exist positive numbers ''δ'' and ''M'' such that

:

If ''g''(''x'') is non-zero for values of ''x'' sufficiently close to ''a'', both of these definitions can be unified using the limit superior:

:$f(x)=O(g(x))\backslash mbox\{\; as\; \}x\; \backslash to\; a\backslash ,$

if and only if

:

Example

In typical usage, the formal definition of ''O'' notation is not used directly; rather, the ''O'' notation for a function ''f''(''x'') is derived by the following simplification rules:

If ''f''(''x'') is a sum of several terms, the one with the largest growth rate is kept, and all others omitted.

If ''f''(''x'') is a product of several factors, any constants (terms in the product that do not depend on ''x'') are omitted.

For example, let $f(x)\; =\; 6x^4\; -\; 2x^3\; +5$, and suppose we wish to simplify this function, using ''O'' notation, to describe its growth rate as ''x'' approaches infinity. This function is the sum of three terms: 6''x''⁴, −2''x''³, and 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of ''x'', namely 6''x''⁴. Now one may apply the second rule: 6''x''⁴ is a product of 6 and ''x''⁴ in which the first factor does not depend on ''x''. Omitting this factor results in the simplified form ''x''⁴. Thus, we say that ''f''(''x'') is a big-oh of (''x''⁴) or mathematically we can write ''f''(''x'') = ''O''(''x''⁴). One may confirm this calculation using the formal definition: let ''f''(''x'') = 6''x''⁴ − 2''x''³ + 5 and ''g''(''x'') = ''x''⁴. Applying the formal definition from above, the statement that ''f''(''x'') = ''O''(''x''⁴) is equivalent to its expansion, :$|f(x)|\; \backslash le\; \backslash ;\; M\; |g(x)|$ for some suitable choice of ''x''₀ and ''M'' and for all ''x'' > ''x''₀. To prove this, let ''x''₀ = 1 and ''M'' = 13. Then, for all ''x'' > ''x''₀: : so :$|6x^4\; -\; 2x^3\; +\; 5|\; \backslash le\; 13\; \backslash ,|x^4\; |.$

Usage

Big O notation has two main areas of application. In mathematics, it is commonly used to describe how closely a finite series approximates a given function, especially in the case of a truncated Taylor series or asymptotic expansion. In computer science, it is useful in the analysis of algorithms. In both applications, the function ''g''(''x'') appearing within the ''O''(...) is typically chosen to be as simple as possible, omitting constant factors and lower order terms. There are two formally close, but noticeably different, usages of this notation: infinite asymptotics and infinitesimal asymptotics. This distinction is only in application and not in principle, however—the formal definition for the "big O" is the same for both cases, only with different limits for the function argument.

Infinite asymptotics

Big O notation is useful when analyzing algorithms for efficiency. For example, the time (or the number of steps) it takes to complete a problem of size ''n'' might be found to be ''T''(''n'') = 4''n''² − 2''n'' + 2. As ''n'' grows large, the ''n''² term will come to dominate, so that all other terms can be neglected — for instance when ''n'' = 500, the term 4''n''² is 1000 times as large as the 2''n'' term. Ignoring the latter would have negligible effect on the expression's value for most purposes. Further, the coefficients become irrelevant if we compare to any other order of expression, such as an expression containing a term n³ or n⁴. Even if ''T''(''n'') = 1,000,000''n''², if ''U''(''n'') = ''n''³, the latter will always exceed the former once ''n'' grows larger than 1,000,000 (''T''(1,000,000) = 1,000,000³= ''U''(1,000,000)). Additionally, the number of steps depends on the details of the machine model on which the algorithm runs, but different types of machines typically vary by only a constant factor in the number of steps needed to execute an algorithm. So the big O notation captures what remains: we write either :$\backslash \; T(n)=\; O(n^2)$ or :$T(n)\backslash in\; O(n^2)$ and say that the algorithm has ''order of n²'' time complexity. Note that "=" is not meant to express "is equal to" in its normal mathematical sense, but rather a more colloquial "is", so the second expression is technically accurate (see the "Equals sign" discussion below) while the first is a common abuse of notation.

Infinitesimal asymptotics

Big O can also be used to describe the error term in an approximation to a mathematical function. The most significant terms are written explicitly, and then the least-significant terms are summarized in a single big O term. For example, :$e^x=1+x+\backslash frac\{x^2\}\{2\}+O(x^3)\backslash qquad\backslash text\{as\; \}\; x\backslash to\; 0$ expresses the fact that the error, the difference $\backslash \; e^x\; -\; (1\; +\; x\; +\; x^2/2)$, is smaller in absolute value than some constant times $|x^3|$ when $x$ is close enough to 0.

Properties

If a function ''f''(''n'') can be written as a finite sum of other functions, then the fastest growing one determines the order of ''f''(''n''). For example :$f(n)\; =\; 9\; \backslash log\; n\; +\; 5\; (\backslash log\; n)^3\; +\; 3n^2\; +\; 2n^3\; =\; O(n^3)\backslash ,\backslash !.$ In particular, if a function may be bounded by a polynomial in ''n'', then as ''n'' tends to ''infinity'', one may disregard ''lower-order'' terms of the polynomial. ''O''(''n''^''c'') and ''O''(''c''^''n'') are very different. The latter grows much, much faster, no matter how big the constant ''c'' is (as long as it is greater than one). A function that grows faster than any power of ''n'' is called ''superpolynomial''. One that grows more slowly than any exponential function of the form $c^n$ is called ''subexponential''. An algorithm can require time that is both superpolynomial and subexponential; examples of this include the fastest known algorithms for integer factorization. ''O''(log ''n'') is exactly the same as ''O''(log(''n''^''c'')). The logarithms differ only by a constant factor (since $\backslash log(n^c)=c\; \backslash log\; n$) and thus the big O notation ignores that. Similarly, logs with different constant bases are equivalent. Exponentials with different bases, on the other hand, are not of the same order. For example, $2^n$ and $3^n$ are not of the same order. Changing units may or may not affect the order of the resulting algorithm. Changing units is equivalent to multiplying the appropriate variable by a constant wherever it appears. For example, if an algorithm runs in the order of ''n''², replacing ''n'' by ''cn'' means the algorithm runs in the order of $c^2n^2$, and the big O notation ignores the constant $c^2$. This can be written as $c^2n^2\; \backslash in\; O(n^2)$. If, however, an algorithm runs in the order of $2^n$, replacing n with cn gives $2^\{cn\}\; =\; (2^c)^n$. This is not equivalent to $2^n$ in general. Changing of variable may affect the order of the resulting algorithm. For example, if an algorithm's running time is ''O''(''n'') when measured in terms of the number ''n'' of ''digits'' of an input number ''x'', then its running time is ''O''(log ''x'') when measured as a function of the input number ''x'' itself, because ''n'' = Θ(log ''x'').

Product

:$f\_1\; \backslash in\; O(g\_1)\; \backslash text\{\; and\; \}\; f\_2\backslash in\; O(g\_2)\backslash ,\; \backslash Rightarrow\; f\_1\; f\_2\backslash in\; O(g\_1\; g\_2)\backslash ,$ :$f\backslash cdot\; O(g)\; \backslash subset\; O(f\; g)$

Sum

:$f\_1\; \backslash in\; O(g\_1)\; \backslash text\{\; and\; \}\; f\_2\backslash in\; O(g\_2)\backslash ,\; \backslash Rightarrow\; f\_1\; +\; f\_2\backslash in\; O(|g\_1|\; +\; |g\_2|)\backslash ,$ ::This implies $f\_1\; \backslash in\; O(g)\; \backslash text\{\; and\; \}\; f\_2\; \backslash in\; O(g)\; \backslash Rightarrow\; f\_1+f\_2\; \backslash in\; O(g)$, which means that $O(g)$ is a convex cone. :If ''f'' and ''g'' are positive functions, $f\; +\; O(g)\; \backslash in\; O(f\; +\; g)$

Multiplication by a constant

:Let ''k'' be a constant. Then: :$\backslash \; O(k\; g)\; =\; O(g)$ if ''k'' is nonzero. :$f\backslash in\; O(g)\; \backslash Rightarrow\; kf\backslash in\; O(g).$

Multiple variables

Big ''O'' (and little o, and Ω...) can also be used with multiple variables. To define Big ''O'' formally for multiple variables, suppose $f(\backslash vec\{x\})$ and $g(\backslash vec\{x\})$ are two functions defined on some subset of $\backslash mathbb\{R\}^n$. We say :$f(\backslash vec\{x\})\backslash mbox\{\; is\; \}O(g(\backslash vec\{x\}))\backslash mbox\{\; as\; \}\backslash vec\{x\}\backslash to\backslash infty$ if and only if :$\backslash exists\; C\backslash ,\backslash exists\; M>0\backslash mbox\{\; such\; that\; \}\; |f(\backslash vec\{x\})|\; \backslash le\; C\; |g(\backslash vec\{x\})|\backslash mbox\{\; for\; all\; \}\backslash vec\{x\}\; \backslash mbox\{\; with\; \}\; x\_i>M\; \backslash mbox\{\; for\; all\; \}i.$ For example, the statement :$f(n,m)\; =\; n^2\; +\; m^3\; +\; O(n+m)\; \backslash mbox\{\; as\; \}\; n,m\backslash to\backslash infty\backslash ,$ asserts that there exist constants ''C'' and ''M'' such that :$\backslash forall\; n,\; m>M\backslash colon\; |g(n,m)|\; \backslash le\; C(n+m),$ where ''g''(''n'',''m'') is defined by :$f(n,m)\; =\; n^2\; +\; m^3\; +\; g(n,m).\backslash ,$ Note that this definition allows all of the coordinates of $\backslash vec\{x\}$ to increase to infinity. In particular, the statement :$f(n,m)\; =\; O(n^m)\; \backslash mbox\{\; as\; \}\; n,m\backslash to\backslash infty\backslash ,$ (i.e., $\backslash exists\; C\backslash ,\backslash exists\; M\backslash ,\backslash forall\; n\backslash ,\backslash forall\; m\backslash dots$) is quite different from :$\backslash forall\; m\backslash colon\; f(n,m)\; =\; O(n^m)\; \backslash mbox\{\; as\; \}\; n\backslash to\backslash infty$ (i.e., $\backslash forall\; m\backslash ,\backslash exists\; C\backslash ,\backslash exists\; M\backslash ,\backslash forall\; n\backslash dots$).

Matters of notation

Equals sign

The statement "''f''(''x'') is ''O''(''g''(''x''))" as defined above is usually written as ''f''(''x'') = ''O''(''g''(''x'')). Some consider this to be an abuse of notation, since the use of the equals sign could be misleading as it suggests a symmetry that this statement does not have. As de Bruijn says, ''O''(''x'') = ''O''(''x''²) is true but ''O''(''x''²) = ''O''(''x'') is not. Knuth describes such statements as "one-way equalities", since if the sides could be reversed, "we could deduce ridiculous things like ''n'' = ''n''² from the identities ''n'' = ''O''(''n''²) and ''n''² = ''O''(''n''²)." For these reasons, it would be more precise to use set notation and write ''f''(''x'') ∈ ''O''(''g''(''x'')), thinking of ''O''(''g''(''x'')) as the class of all functions ''h''(''x'') such that |''h''(''x'')| ≤ ''C''|''g''(''x'')| for some constant ''C''. However, the use of the equals sign is customary. Knuth pointed out that "mathematicians customarily use the = sign as they use the word 'is' in English: Aristotle is a man, but a man isn't necessarily Aristotle."

Other arithmetic operators

Big O notation can also be used in conjunction with other arithmetic operators in more complicated equations. For example, ''h''(''x'') + ''O''(''f''(''x'')) denotes the collection of functions having the growth of ''h''(''x'') plus a part whose growth is limited to that of ''f''(''x''). Thus, :$g(x)\; =\; h(x)\; +\; O(f(x))\backslash ,$ expresses the same as :$g(x)\; -\; h(x)\; \backslash in\; O(f(x))\backslash ,.$

Example

Suppose an algorithm is being developed to operate on a set of ''n'' elements. Its developers are interested in finding a function ''T''(''n'') that will express how long the algorithm will take to run (in some arbitrary measurement of time) in terms of the number of elements in the input set. The algorithm works by first calling a subroutine to sort the elements in the set and then perform its own operations. The sort has a known time complexity of ''O''(''n''²), and after the subroutine runs the algorithm must take an additional $55n^3+2n+10$ time before it terminates. Thus the overall time complexity of the algorithm can be expressed as :$T(n)=O(n^2)+55n^3+2n+10.\backslash$ This can perhaps be most easily read by replacing ''O''(''n''²) with "some function that grows asymptotically no faster than ''n''² ". Again, this usage disregards some of the formal meaning of the "=" and "+" symbols, but it does allow one to use the big O notation as a kind of convenient placeholder.

Declaration of variables

Another feature of the notation, although less exceptional, is that function arguments may need to be inferred from the context when several variables are involved. The following two right-hand side big O notations have dramatically different meanings: :$f(m)\; =\; O(m^n)\backslash ,,$ :$g(n)\backslash ,\backslash ,\; =\; O(m^n)\backslash ,.$ The first case states that ''f''(''m'') exhibits polynomial growth, while the second, assuming ''m'' > 1, states that ''g''(''n'') exhibits exponential growth. To avoid confusion, some authors use the notation :$g(x)\; \backslash in\; O(f(x))\backslash ,.$ rather than the less explicit :$g\; \backslash in\; O(f)\backslash ,,$

Multiple usages

In more complicated usage, ''O''(...) can appear in different places in an equation, even several times on each side. For example, the following are true for $n\backslash to\backslash infty$ :$(n+1)^2\; =\; n^2\; +\; O(n)\backslash$ :$(n+O(n^\{1/2\}))(n\; +\; O(\backslash log\; n))^2\; =\; n^3\; +\; O(n^\{5/2\})\backslash$ :$n^\{O(1)\}\; =\; O(e^n).\backslash$ The meaning of such statements is as follows: for ''any'' functions which satisfy each ''O''(...) on the left side, there are ''some'' functions satisfying each ''O''(...) on the right side, such that substituting all these functions into the equation makes the two sides equal. For example, the third equation above means: "For any function $f(n)=O(1)\backslash ,$, there is some function $g(n)=O(e^n)\backslash ,$ such that $n^\{f(n)\}=g(n)$." In terms of the "set notation" above, the meaning is that the class of functions represented by the left side is a subset of the class of functions represented by the right side. In this use the "=" is a formal symbol that unlike the usual use of "=" is not a symmetric relation. Thus for example $n^\{O(1)\}\; =\; O(e^n)\backslash ,$ does not imply the false statement $O(e^n)\; =\; n^\{O(1)\}\backslash ,$.

Orders of common functions

Here is a list of classes of functions that are commonly encountered when analyzing the running time of an algorithm. In each case, ''c'' is a constant and ''n'' increases without bound. The slower-growing functions are generally listed first.

!Notation !Logarithmic timelinear timepolynomial time

Name !! Example
$O(1)\backslash ,$	Constant time>constant	Determining if a number is even or odd; using a constant-size lookup table or hash table
$O(\backslash log\; \backslash log\; n)\backslash ,$	double logarithmic
$O(\backslash log\; n)\backslash ,$	logarithmic || Finding an item in a sorted array with a binary search or a balanced search tree as well as all operations in a Binomial heap.
	fractional power
$O(n)\backslash ,$	linear || Finding an item in an unsorted list or a malformed tree (worst case) or in an unsorted array; Adding two n-bit integers by ripple carry.
$O(n\backslash log\; n)=O(\backslash log\; n!)\backslash ,$	Linearithmic time>linearithmic, loglinear, or quasilinear
$O(n^2)\backslash ,$	quadratic time>quadratic
$O(n^c),\backslash ;c>1$	polynomial or algebraic || Tree-adjoining grammar parsing; maximum matching for bipartite graphs
$e^\{(c+o(1))\; (\backslash ln\; n)^\backslash alpha\; (\backslash ln\; \backslash ln\; n)^\{1-\backslash alpha\}\}$	L-notation or sub-exponential time>sub-exponential
$O(c^n),\backslash ;c>1$	exponential time>exponential
$O(n!)\backslash ,$	factorial

The statement $f(n)=O(n!)\backslash ,$ is sometimes weakened to $f(n)=O\backslash left(n^n\backslash right)$ to derive simpler formulas for asymptotic complexity. For any $k>0$ and $c>0$, $O(n^c(\backslash log\; n)^k)$ is a subset of $O(n^\{c+\backslash varepsilon\; \})$ for any $\backslash varepsilon\; >0$, so may be considered as a polynomial with some bigger order.

Related asymptotic notations

Big ''O'' is the most commonly used asymptotic notation for comparing functions, although in many cases Big ''O'' may be replaced with Big Theta Θ for asymptotically tighter bounds. Here, we define some related notations in terms of Big ''O'', progressing up to the family of Bachmann–Landau notations to which Big ''O'' notation belongs. ===Little-o notation=== The relation $f(x)\; \backslash in\; o(g(x))$ is read as "$f(x)$ is little-o of $g(x)$". Intuitively, it means that $g(x)$ grows much faster than $f(x)$, or similarly, the growth of $f(x)$ is nothing compared to that of $g(x)$. It assumes that ''f'' and ''g'' are both functions of one variable. Formally, ''f''(''n'') = ''o''(''g''(''n'')) as means that for every positive constant ''ε'' there exists a constant ''N'' such that :$|f(n)|\backslash leq\backslash epsilon|g(n)|\backslash qquad\backslash text\{for\; all\; \}n\backslash geq\; N~.$

Note the difference between the earlier formal definition for the big-O notation, and the present definition of little-o: while the former has to be true for ''at least one'' constant ''M'' the latter must hold for ''every'' positive constant ''ε'', however small. In this way little-o notation makes a stronger statement than the corresponding big-O notation: every function that is little-o of ''g'' is also big-O of ''g'', but not every function that is big-O ''g'' is also little-o of ''g'' (for instance ''g'' itself is not, unless it is identically zero near ∞).

If ''g''(''x'') is nonzero, or at least becomes nonzero beyond a certain point, the relation ''f''(''x'') = ''o''(''g''(''x'')) is equivalent to :$\backslash lim\_\{x\; \backslash to\; \backslash infty\}\backslash frac\{f(x)\}\{g(x)\}=0.$ For example,

$2x\; \backslash in\; o(x^2)\; \backslash ,\backslash !$

$2x^2\; \backslash not\; \backslash in\; o(x^2)$

$1/x\; \backslash in\; o(1)$

Little-o notation is common in mathematics but rarer in computer science. In computer science the variable (and function value) is most often a natural number. In mathematics, the variable and function values are often real numbers. The following properties can be useful:

$o(f)\; +\; o(f)\; \backslash subseteq\; o(f)$

$o(f)o(g)\; \backslash subseteq\; o(fg)$

$o(o(f))\; \backslash subseteq\; o(f)$

$o(f)\; \backslash subset\; O(f)$ (and thus the above properties apply with most combinations of o and O).

As with big O notation, the statement "$f(x)$ is $o(g(x))$" is usually written as $f(x)\; =\; o(g(x))$, which is a slight abuse of notation.

Family of Bachmann–Landau notations

! Notation	! Name	! Intuition	! Informal definition: for sufficiently large $n$...	! Formal Definition	! Notes
$f(n)\; \backslash in\; O(g(n))$	Big Omicron; Big O; Big Oh	$f$ is bounded above by $g$ (up to constant factor) asymptotically		$$	or $\backslash exists\; k>0\; \backslash ;\; \backslash exists\; n\_0\; \backslash ;\; \backslash forall\; n>n\_0\; \backslash ;\; f(n)\; \backslash leq\; g(n)\backslash cdot\; k$
$f(n)\; \backslash in\; \backslash Omega(g(n))$	Big Omega	$f$ is bounded below by $g$ (up to constant factor) asymptotically	$f(n)\; \backslash geq\; g(n)\backslash cdot\; k$ for some positive ''k''		$\backslash exists\; k>0\; \backslash ;\; \backslash exists\; n\_0\; \backslash ;\; \backslash forall\; n>n\_0\; \backslash ;\; g(n)\backslash cdot\; k\; \backslash leq\; f(n)$	Since the beginning of the 20th century, papers in number theory have been increasingly and widely using this notation in the weaker sense that ''f'' = o(''g'') is false.
$f(n)\; \backslash in\; \backslash Theta(g(n))$	Big Theta	$f$ is bounded both above and below by $g$ asymptotically	$g(n)\backslash cdot\; k\_1\; \backslash leq\; f(n)\; \backslash leq\; g(n)\backslash cdot\; k\_2$ for some positive ''k''1, ''k''2			$\backslash exists\; k\_1>0\; \backslash ;\; \backslash exists\; k\_2>0\; \backslash ;\; \backslash exists\; n\_0\; \backslash ;\; \backslash forall\; n>n\_0$	$g(n)\; \backslash cdot\; k\_1\; \backslash leq\; f(n)\; \backslash leq\; g(n)\; \backslash cdot\; k\_2$
$f(n)\; \backslash in\; o(g(n))$	Small Omicron; Small O; Small Oh	$f$ is dominated by $g$ asymptotically	$|f(n)|\; \backslash le\; |g(n)|\backslash cdot\; \backslash varepsilon$ for every $\backslash varepsilon$			$\backslash forall\; \backslash varepsilon>0\; \backslash ;\; \backslash exists\; n\_0\; \backslash ;\; \backslash forall\; n>n\_0\; \backslash ;\; |f(n)|\; \backslash le\; |g(n)\backslash cdot\; \backslash varepsilon|$
$f(n)\; \backslash in\; \backslash omega(g(n))$	Small Omega	$f$ dominates $g$ asymptotically	$f(n)\; \backslash ge\; g(n)\backslash cdot\; k$ for every ''k''
$f(n)\backslash sim\; g(n)\backslash !$	On the order of	$f$ is equal to $g$ asymptotically	$f(n)/g(n)\; \backslash to\; 1$	$\backslash forall\; \backslash varepsilon>0\backslash ;\backslash exists\; n\_0\backslash ;\backslash forall\; n>n\_0\backslash ;\backslash left$

Bachmann–Landau notation was designed around several mnemonics, as shown in the ''As $n\; \backslash to\; \backslash infty$, eventually...'' column above and in the bullets below. To conceptually access these mnemonics, "omicron" can be read "o-''micro''n" and "omega" can be read "o-''mega''". Also, the lower-case versus capitalization of the Greek letters in Bachmann–Landau notation is mnemonic.

The ''o-micron mnemonic'': The o-''micro''n reading of $f(n)\; \backslash in\; O(g(n))$ and of $f(n)\; \backslash in\; o(g(n))$ can be thought of as "O-''smaller than''" and "o-''smaller than''", respectively. This ''micro''/smaller mnemonic refers to: for sufficiently large input parameter(s), $f$ grows at a rate that may henceforth be less than $cg$ regarding $g\; \backslash in\; O(f)$ or $g\; \backslash in\; o(f)$.

The ''o-mega mnemonic'': The o-''mega'' reading of $f(n)\; \backslash in\; \backslash Omega(g(n))$ and of $f(n)\; \backslash in\; \backslash omega(g(n))$ can be thought of as "O-''larger than''". This ''mega''/larger mnemonic refers to: for sufficiently large input parameter(s), $f$ grows at a rate that may henceforth be greater than $cg$ regarding $g\; \backslash in\; \backslash Omega(f)$ or $g\; \backslash in\; \backslash omega(f)$.

The ''upper-case mnemonic'': This mnemonic reminds us when to use the upper-case Greek letters in $f(n)\; \backslash in\; O(g(n))$ and $f(n)\; \backslash in\; \backslash Omega(g(n))$: for sufficiently large input parameter(s), $f$ grows at a rate that may henceforth be equal to $cg$ regarding $g\; \backslash in\; O(f)$.

The ''lower-case mnemonic'': This mnemonic reminds us when to use the lower-case Greek letters in $f(n)\; \backslash in\; o(g(n))$ and $f(n)\; \backslash in\; \backslash omega(g(n))$: for sufficiently large input parameter(s), $f$ grows at a rate that is henceforth inequal to $cg$ regarding $g\; \backslash in\; O(f)$.

Aside from Big ''O'' notation, the Big Theta Θ and Big Omega Ω notations are the two most often used in computer science; the Small Omega ω notation is rarely used in computer science.

Use in computer science

Informally, especially in computer science, the Big ''O'' notation often is permitted to be somewhat abused to describe an asymptotic tight bound where using Big Theta Θ notation might be more factually appropriate in a given context. For example, when considering a function $T(n)\; =\; 73n^3\; +\; 22n^2\; +\; 58$, all of the following are generally acceptable, but tightnesses of bound (i.e., bullets 2 and 3 below) are usually strongly preferred over laxness of bound (i.e., number 1 below). #''T''(''n'') = ''O''(''n''¹⁰⁰), which is identical to ''T''(''n'') ∈ ''O''(''n''¹⁰⁰) #''T''(''n'') = ''O''(''n''³), which is identical to ''T''(''n'') ∈ ''O''(''n''³) #''T''(''n'') = Θ(''n''³), which is identical to ''T''(''n'') ∈ Θ(''n''³). The equivalent English statements are respectively: #''T''(''n'') grows asymptotically no faster than ''n''¹⁰⁰ #''T''(''n'') grows asymptotically no faster than ''n''³ #''T''(''n'') grows asymptotically as fast as ''n''³. So while all three statements are true, progressively more information is contained in each. In some fields, however, the Big O notation (number 2 in the lists above) would be used more commonly than the Big Theta notation (bullets number 3 in the lists above) because functions that grow more slowly are more desirable. For example, if $T(n)$ represents the running time of a newly developed algorithm for input size $n$, the inventors and users of the algorithm might be more inclined to put an upper asymptotic bound on how long it will take to run without making an explicit statement about the lower asymptotic bound.

Extensions to the Bachmann–Landau notations

Another notation sometimes used in computer science is Õ (read ''soft-O''): ''f''(''n'') = ''Õ''(''g''(''n'')) is shorthand for ''f''(''n'') = ''O''(''g''(''n'') log^''k'' ''g''(''n'')) for some ''k''. Essentially, it is Big O notation, ignoring logarithmic factors because the growth-rate effects of some other super-logarithmic function indicate a growth-rate explosion for large-sized input parameters that is more important to predicting bad run-time performance than the finer-point effects contributed by the logarithmic-growth factor(s). This notation is often used to obviate the "nitpicking" within growth-rates that are stated as too tightly bounded for the matters at hand (since log^''k'' ''n'' is always ''o''(''n''^ε) for any constant ''k'' and any ε > 0). The L notation, defined as :$L\_n[\backslash alpha,c]=O\backslash left(e^\{(c+o(1))(\backslash ln\; n)^\backslash alpha(\backslash ln\backslash ln\; n)^\{1-\backslash alpha\}\}\backslash right),$ is convenient for functions that are between polynomial and exponential.

Generalizations and related usages

The generalization to functions taking values in any normed vector space is straightforward (replacing absolute values by norms), where ''f'' and ''g'' need not take their values in the same space. A generalization to functions ''g'' taking values in any topological group is also possible. The "limiting process" ''x→x_o'' can also be generalized by introducing an arbitrary filter base, i.e. to directed nets ''f'' and ''g''. The ''o'' notation can be used to define derivatives and differentiability in quite general spaces, and also (asymptotical) equivalence of functions, :$f\backslash sim\; g\; \backslash iff\; (f-g)\; \backslash in\; o(g)$ which is an equivalence relation and a more restrictive notion than the relationship "''f'' is Θ(''g'')" from above. (It reduces to $\backslash lim\; f/g\; =\; 1$ if ''f'' and ''g'' are positive real valued functions.) For example, 2''x'' is Θ(''x''), but 2''x'' − ''x'' is not ''o''(''x'').

Graph theory

It is often useful to bound the running time of graph algorithms. Unlike most other computational problems, for a graph ''G'' = (''V'', ''E'') there are two relevant parameters describing the size of the input: the number |''V''| of vertices in the graph and the number |''E''| of edges in the graph. Inside asymptotic notation (and only there), it is common to use the symbols ''V'' and ''E'', when someone really means |''V''| and |''E''|. This convention simplifies asymptotic functions and make them easily readable. The symbols ''V'' and ''E'' are never used inside asymptotic notation with their literal meaning, since the number of vertices and edges must be non-negative, so this abuse of notation does not risk ambiguity. For example $O(E\; +\; V\; \backslash log\; V)\backslash ,$ means $O((V,E)\; \backslash mapsto\; |E|\; +\; |V|\backslash cdot\backslash log|V|)\backslash ,$ for a suitable metric of graphs. Another common convention—referring to the values |''V''| and |''E''| by the names ''n'' and ''m'', respectively—sidesteps this ambiguity.

History

The notation was first introduced by number theorist Paul Bachmann in 1894, in the second volume of his book ''Analytische Zahlentheorie'' ("analytic number theory"), the first volume of which (not yet containing big O notation) was published in 1892. The notation was popularized in the work of number theorist Edmund Landau; hence it is sometimes called a Landau symbol. It was popularized in computer science by Donald Knuth, who re-introduced the related Omega and Theta notations. He also noted that the (then obscure) Omega notation had been introduced by Hardy and Littlewood under a slightly different meaning, and proposed the current definition. Hardy's symbols were (in terms of the modern ''O'' notation) :$f\backslash lesssim\; g\; \backslash iff\; f\; \backslash in\; O(g)$   and   $f\backslash ll\; g\; \backslash iff\; f\backslash in\; o(g);$ other similar symbols were sometimes used, such as $\backslash preceq$ and $\backslash prec\backslash !\backslash !\backslash !\backslash !\backslash !\backslash !\backslash !\backslash !\backslash prec$. The big-O, standing for "order of", was originally a capital omicron; today the identical-looking Latin capital letter O is used, but never the digit zero.

See also

Asymptotic expansion: Approximation of functions generalizing Taylor's formula

Asymptotically optimal: A phrase frequently used to describe an algorithm that has an upper bound asymptotically within a constant of a lower bound for the problem

Limit superior and limit inferior: An explanation of some of the limit notation used in this article

Nachbin's theorem: A precise method of bounding complex analytic functions so that the domain of convergence of integral transforms can be stated

Big O in probability notation: ''O_p'',''o_p''

Computational complexity theory: A sub-field strongly related to this article

References

Further reading

Paul Bachmann. ''Die Analytische Zahlentheorie. Zahlentheorie''. pt. 2 Leipzig: B. G. Teubner, 1894.

Edmund Landau. ''Handbuch der Lehre von der Verteilung der Primzahlen''. 2 vols. Leipzig: B. G. Teubner, 1909.

G. H. Hardy. ''Orders of Infinity: The 'Infinitärcalcül' of Paul du Bois-Reymond'', 1910.

Donald Knuth. ''The Art of Computer Programming'', Volume 1: ''Fundamental Algorithms'', Third Edition. Addison-Wesley, 1997. ISBN 0-201-89683-4. Section 1.2.11: Asymptotic Representations, pp. 107–123.

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. ''Introduction to Algorithms'', Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0-262-03293-7. Section 3.1: Asymptotic notation, pp. 41–50.

Pages 226–228 of section 7.1: Measuring complexity.

Jeremy Avigad, Kevin Donnelly. ''Formalizing O notation in Isabelle/HOL''

Paul E. Black, "big-O notation", in ''Dictionary of Algorithms and Data Structures'' [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 11 March 2005. Retrieved December 16, 2006.

Paul E. Black, "little-o notation", in ''Dictionary of Algorithms and Data Structures'' [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. Retrieved December 16, 2006.

Paul E. Black, "Ω", in ''Dictionary of Algorithms and Data Structures'' [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. Retrieved December 16, 2006.

Paul E. Black, "ω", in ''Dictionary of Algorithms and Data Structures'' [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 29 November 2004. Retrieved December 16, 2006.

Paul E. Black, "Θ", in ''Dictionary of Algorithms and Data Structures'' [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. Retrieved December 16, 2006.

External links

Introduction to Asymptotic Notations

Landau Symbols

Category:Mathematical notation Category:Asymptotic analysis Category:Analysis of algorithms

bn:বড় O লিখনপদ্ধতি ca:Cota superior asimptòtica cs:Asymptotická složitost de:Landau-Symbole es:Cota superior asintótica eo:Granda O fa:نماد O بزرگ fr:Comparaison asymptotique ko:점근 표기법 id:Notasi O besar it:O-grande he:סימון אסימפטוטי hu:O jelölés nl:Grote-O-notatie ja:ランダウの記号 no:Stor O-notasjon pl:Asymptotyczne tempo wzrostu pt:Grande-O ru:«O» большое и «o» малое simple:Big O notation sr:Велико О fi:Asymptoottinen suoritusaika sv:Ordo th:สัญกรณ์โอใหญ่ tr:Büyük O gösterimi uk:Нотація Ландау vi:Kí hiệu O lớn zh:大O符号

}} Cameron Leslie, MNZM (born 17 January 1990 in Whangarei, New Zealand) is a New Zealand paralympics swimmer, most notable for his performance at the 2008 Summer Paralympics, winning a gold medal in the men's 150 m individual medley, in which his time of 2:33.57 broke the previous world record by over a second. Leslie is a student at Auckland University of Technology and has a quadruple limb deficiency. Leslie says he may leave swimming to play wheelchair rugby in later games.

Footnotes

Category:1990 births Category:Living people Category:Members of the New Zealand Order of Merit Category:New Zealand swimmers Category:Paralympic swimmers of New Zealand Category:Paralympic gold medalists for New Zealand Category:World record holders in paralympic swimming

name	Adrian Lewis
fullname	Adrian Lewis
nickname	Jackpot
birth date	January 21, 1985
birth place	Stoke-on-Trent, England
hometown	Stoke-on-Trent
homecountry	England
since	2003
darts	21g Target 'Adrian Lewis'
laterality	Right-handed
music	Reach Up (Papa's Got A Brand New Pigbag) by Perfecto Allstarz
bdo	2002–2003
pdc	2003 – Present
currentrank	2
world darts trophy	Round 2 2007
int. darts league	Semi Finalist 2007
pdc world	Winner (2) 2011, 2012
matchplay	Semi Finalist (2) 2007, 2011
european	Runner Up (2) 2008, 2011
grand prix	Runner Up 2010
uk open	Quarter Finalist 2010
vegas	Quarter Finalist (2) 2007, 2009
premier league	Runner Up 2011
grand slam	Semi Finalist 2011
championship league	Initial groups, Runner-up 2008
pc finals	Quarter Finalist 2010
tournament	British Teenage OpenChris de Roo OpenPlayers Championship (AUT)Players Championship (CRA)Players Championship (GER)Players Championship (IRE)Players Championship (SCO)UK Open QualifierUK Open Scottish Regional FinalWorld Cup of Darts
resultyears	2003200420092010201020092005, 2006201120052012
updated	}}

Adrian Lewis (born 21 January 1985 in Stoke-on-Trent) is an English professional darts player for the Professional Darts Corporation (PDC) who is the reigning two time PDC World Darts Champion. He is nicknamed Jackpot, following a visit to a casino whilst competing at the 2005 Las Vegas Desert Classic when he "won" a $72,000 jackpot but was unable to claim the money as he was under-age by US gaming laws – despite being eligible in the UK. During the early part of his career until 2007, he was a protégé of multi-world champion Phil Taylor having practised together in their home city Stoke-on-Trent and made his television debut in 2004, aged 19 at the UK Open.

Early career

Lewis had shown his potential at the age of 18 by winning the 2003 British Teenage Open and after competing at the 2003 Winmau World Masters he joined the PDC without ever qualifying or playing in the Lakeside World Championship.

Lewis reached a semi-final of the regional qualifiers for the UK Open in 2004, which provided his opportunity for a television debut at the 2004 UK Open in Bolton, where he narrowly lost his last 64 match to Dennis Harbour. His next television appearance came against his mentor Taylor at the 2004 Las Vegas Desert Classic where he went out 0–2 in the first round. He then went on to win his first match on television at the 2004 World Grand Prix beating former world champion Richie Burnett.

He failed to qualify for the 2005 PDC World Championships but back at Bolton for the UK Open he produced one of the rare whitewashes in the tournament history, beating Colin Monk 11–0 before falling to Chris Mason in the last 16. His World Matchplay debut came in 2005 and reached the quarter-finals before losing to Colin Lloyd.

Major Breakthrough

During 2005, Lewis began to produce some promising results including a run to the quarter-finals of the 2005 World Matchplay. Towards the end of 2005, he matched Phil Taylor by winning both PDC Pro Tour events during a weekend in Scotland by taking the PDPA Players Championship and the UK Open Scottish Regional titles.

Lewis made his PDC World Championship debut in 2006, where he reached the quarter-finals by defeating Dave Honey, Dennis Priestley and Roland Scholten. He was involved in, what has become, an infamous match against Peter Manley. When 1–2 down Lewis successfully hit a blind 180, where he turned to face Manley as the last dart was in the air. Manley won the set and then appeared to say something while Lewis was throwing, which caused him to leave the stage. Lewis did return, but went on to lose the match 3–5.

His biggest breakthrough came in May 2006 when he joined the 15 other PDC players in the top 16 competing against 16 American qualifiers in the World Series of Darts which was broadcast on ESPN. Lewis' performance in this tournament made others refer to him as a major threat in years to come. He beat Lloyd, Denis Ovens and Priestley before falling in the final to Taylor.

His ranking continued to rise by reaching the later stages of the non-televised PDC Pro Tour events during 2006 as well as the quarter-finals of the UK Open in 2006 where he beat Wayne Mardle 11–10 in the last 16, before losing to John MaGowan 11–8 in the last eight.

2007–2010

Between 2007 and 2010, Lewis produced inconsistent form and was often unable to follow up on big wins such as the 2007 World Matchplay in Blackpool where he beat the incumbent world champion Raymond van Barneveld 16–14 in the quarter finals before losing heavily 7–17 in the semi finals to James Wade.

He lost to Andy Jenkins in the last 16 of the 2007 World Championship, but was selected by Sky Sports as a wildcard for the 2007 Premier League. The event is prestigious as it involves the top 7 PDC players and the aforementioned wildcard. Lewis finished seventh in the league, winning five of his fourteen matches.

He reached the quarter-finals of the World Championship for the second time in 2008, but was defeated 2–5 by Kevin Painter. At the 2008 European Darts Championship, Lewis played his first-round match against Hannes Schnier with three plasters on his non-throwing hand – having attempted to catch a falling glass backstage but shattered in his hand. After winning the match 5–2, Lewis was taken to hospital for checks on two deep cuts. Lewis went on to beat Ovens 9–5 in the 2nd round, before producing arguably the best performance of his career with a 9–2 victory over van Barneveld in the quarter-finals. An 11–7 victory over Manley set up a final with Taylor. Lewis lost 11–5 but his performance in the tournament guaranteed him a place in the 2008 Grand Slam of Darts.

Lewis was defeated in the second round of the 2009 World Championship, 3–4 by Paul Nicholson but did manage to end his title drought in September. He won his first PDC Pro Tour event in three years at the Austrian Players Championship, where he beat Carlos Rodriguez 6–4 in the final, which included a nine dart finish. He dedicated victory to his one month old daughter. He added another Pro Tour title the following month at the Irish Open Players Championship beating Andy Hamilton in the final by 6 legs to 4.

His form on television also improved during 2009 reaching the quarter finals of the Las Vegas Desert Classic, World Matchplay and World Grand Prix. During 2010 he also made the last eight of the World Championship, Players Championships and UK Open before reaching his first televised final on Sky Television in the 2010 World Grand Prix where he beat Phil Taylor for the first time on television in the semi finals but lost to James Wade in the final. There were further title successes in 2010, when he won Players Championships in Crawley and Germany to bring his overall Pro Tour title tally to seven.

2011 season

World Championship win

Lewis reached the final of the 2011 PDC World Darts Championship courtesy of victories over Tony Eccles, Mark Dudbridge, Robert Thornton, Vincent van der Voort and Mark Webster en route to the final, where he played Gary Anderson. The match-up ensured that, for the first time, the winner of the PDC World Championship would not have previously succeeded in the rival BDO World Championship. Lewis himself became the only player to have reached the PDC final without playing full-time on the BDO circuit.

During the first set of the match, Lewis became the first player to throw a nine dart finish in a World Championship final. Lewis went on to win the match 7–5 and with it the championship, guaranteeing him a place in the 2011 Premier League. He has also risen to his highest ranking of no.2. In addition, at 25 years old Lewis became the fifth youngest player to win a World Championship, behind Jelle Klaasen (21 in 2006), Eric Bristow (22 in 1980), Keith Deller (23 in 1983), and Mark Webster (24 in 2008), as well as the youngest ever PDC World Champion.

Rest of 2011

In the 2011 Players Championship Finals Lewis lost 6–4 to Steve Beaton in the first round.

Lewis signed a one-year sponsorship deal with pawnbroker Albemarle & Bond in January 2011.

He got off to a winning start in the 2011 premier league of darts by beating the 2010 champion Phil Taylor 8–2, only to lose to Taylor 8–3 in their second meeting. Week 4 saw him get his first heavy defeat of the 2011 campaign, losing 8–2 to Mark Webster. He went on to defeat Gary Anderson in Anderson's home country of Scotland after both players were distracted by the crowd. Lewis was being booed and coins were thrown at him but he went on to win the match 8–3 and both players stated their disappointment with the crowd. During his walk on he had beer thrown over him. Lewis proceeded to make it to the final of the 2011 Premier League but lost 10–4 to Gary Anderson after beating Phil Taylor 8–3 in the semi final in the same night.

Lewis was eliminated in the third round of the 2011 U.K. Open by Terry Jenkins, who took a 9–7 match. He lost 17–10 in the semi-finals of the 2011 World Matchplay to James Wade. He hit another perfect 9 dart leg on the 31st July 2011 at the European Darts Championships against Raymond van Barneveld during their semi- final match which he won 11–10. He played Phil Taylor in the final and lost 8–11.

In the 2011 World Grand Prix, he played John Part in his first round match. He lost 2 sets to 1 after leading 1–0 in sets and 2–0 in legs.

He reached the final of the first players championship in Derby and was defeated 6–2 by Jamie Caven. In the Crawley Players Championship he was defeated in the final by Paul Nicholson 6–4 in a hard fought match, he had defeated Ronnie Baxter 6–5 in the semi final.

Lewis was now under the management of former World Champion Keith Deller and under his guidance he has appeared in several major finals, including his World Championship win.

2012 season

Defending his title

Lewis became the third player, after Eric Bristow and Raymond van Barneveld, to successfully defend their first World Championship title in the 2012 PDC World Championship, by beating Andy Hamilton 7–3 in the Final.

He almost exited the tournament on multiple occasions, beginning with his first round match against Nigel Heydon. He trailed 0–2 and was stung by a wasp during a break on his non-throwing hand, but nevertheless managed to claw his way back to 2–2. Heydon led 2–1 in the deciding set, but never had a dart for the match as Lewis won four of the last five legs to avoid an early exit. More comfortable victories ensued over Robert Thornton (4–2) and Wayne Jones (4–0), with Lewis seemingly heading for the semi-finals as he led Terry Jenkins 3–0 in the last 8, having only lost 2 legs. However, his opponent stormed back to level the match, before Lewis rediscovered his form to win the last two sets and clinch a 5–3 win. He said after the match that he had "lost his way" during Jenkins' fightback, but was delighted to be in the semi-finals.

His semi-final match with James Wade was hailed as one of the greatest comebacks of all time. Lewis trailed both 2–0 and 5–1, only to win the next 5 sets, including 10 straight legs, to incredibly win 6–5 and finished with a 161 checkout. After the semi-final Lewis stated: "That was the best win of my career, definitely".

The match eventually finished at 12:50am (GMT) and with Lewis required to give a drug test upon its completion, he stated he only got 4 hours sleep after going to bed at 5am. However, Lewis managed to never trail against Hamilton and was a double 12 away from hitting a nine-darter in the final for the second successive year. Lewis clinched victory with his third attempt at the match winning double and said afterwards he believed he could win 10 World Championship titles.

The tournament victory took Lewis' career prize money above the £1 million mark, and confirmed his number two status in the PDC Order of Merit. His semi-final comeback was named PDC Televised Performance of the Year at the PDC annual awards ceremony on 3 January.

Rest of 2012

Lewis maintained his form for his next tournament of the season as he represented England and won the 2012 PDC World Cup of Darts, with Phil Taylor. The pair needed a sudden-death leg to see off Canada in the second round, before defeating the United States and Wales to reach the final where they played the Australian team consisting of Simon Whitlock and Paul Nicholson. The final finished with the scores at 3–3 meaning that a sudden-death leg was required to decide the title. Australia missed four darts to take the crown and England two, before Lewis took out double 5 to win his first World Cup, stating that the victory meant more to him than his second world title won a month earlier.

Lewis was an automatic entrant for the 2012 Premier League. He drew his first match with Phil Taylor (who averaged 112) having led 6-1. He then drew his next two matches against Raymond van Barneveld and Andy Hamilton, before being heavily defeated 8-1 by defending champion Gary Anderson

World Championship Results

2006: Quarter-Finals (lost to Peter Manley 3–5)

2007: Third Round (lost to Andy Jenkins 3–4)

2008: Quarter-Finals (lost to Kevin Painter 2–5)

2009: Second Round (lost to Paul Nicholson 3–4)

2010: Quarter-Finals (lost to Phil Taylor 0–5)

2011: Winner (beat Gary Anderson 7–5)

2012: Winner (beat Andy Hamilton 7–3)

Controversies

Lewis has been involved in several controversial matches during his career, including his debut World Championship in 2006. During his quarter final with Peter Manley he decided to leave the stage part-way through the match as he alleged Manley had been trying to upset him whilst he was throwing.

In April 2008, he argued with Kevin Painter during their quarter final match at the Holland Masters. This resulted in a 6 months ban for Lewis, as well as a 4 months suspension and a fine of £400.

At the 2009 World Grand Prix Lewis was playing Gary Anderson in the second round and during the first set the two players exchanged words after Anderson felt Lewis went into the exclusion zone while Anderson was throwing. Lewis won the match 3–2.

The final of the 2010 World Grand Prix saw Lewis in an ill-tempered clash which eventually he lost 3–6 to James Wade. Lewis accused Wade of putting off his throw, by "stamping" on the oche. The pair exchanged a brief handshake, which Wade appeared to look reluctant about. Lewis had also been involved in an incident with Taylor, just 24 hours earlier, during their semi-final match, where Taylor accused Lewis of playing up to the crowd to put him off.

During the 2012 PDC World Darts Championship, both Lewis and his opponent James Wade left the stage with Lewis trailing 2–0 in sets, after complaining of a 'draft' blowing across the stage. The 25 minute break seemed to provoke the crowd into heckling Lewis for the remainder of the game, Lewis went on to win the match 6–5.

Ranking and earnings

Lewis has risen to second in the PDC Order of Merit – the PDC's world ranking system, and has been ranked 2nd since beating Gary Anderson to win his first World Championship final. He has won £1,153,717 during his six year career.

Personal life

His first daughter, Myla Niamh was born in August 2009. In 2011, within a few days after winning the world championship, he broke up with his girlfriend. He supports his local football team .

Performance timeline

! Tournament !! 2003 !! 2004 !! 2005 !! 2006 !! 2007 in darts

2007 !! 2008 !! 2009 !! 2010 !! 2011 !! 2012
style="background:#efefef;"
style="background:#efefef;"
style="background:#efefef;"
style="background:#efefef;"
style="background:#efefef;"
style="background:#efefef;"

References

External links

Official Website

Adrian Lewis' profile and stats on Darts Database

Category:Living people Category:1985 births Category:English darts players Category:Sportspeople from Stoke-on-Trent Category:Professional Darts Corporation players Category:World darts champions

de:Adrian Lewis nl:Adrian Lewis pl:Adrian Lewis ru:Льюис, Адриан

honorific-prefix	The Honourable
name	Hedy Fry
honorific-suffix	PC, MP
term start	1993
predecessor	Kim Campbell
birth date	August 06, 1941
birth place	San Fernando, Trinidad and Tobago
profession	Physician
party	Liberal
party colour	Liberal
residence	Vancouver
riding	Vancouver Centre
religion	Catholic (lapsed)

Hedy Fry, PC, MP (born August 6, 1941) is a Canadian politician and physician. She is the Member of Parliament for Vancouver Centre.

Early life

Fry was born into poverty in San Fernando, Trinidad and Tobago. Declining an English Literature scholarship to Oxford, Fry instead earned her equivalent of a BA in Science in one year and went on to then receive her medical training at the Royal College of Surgeons in Dublin, Ireland. She emigrated to Canada and established a practice in Vancouver. She served as president of the British Columbia Federation of Medical Women in 1977. She was president of the Vancouver Medical Association in 1988-89, the BC Medical Association in 1990-91, and chaired the Canadian Medical Association's Multiculturalism Committee in 1992-9. Fry was also a host on the nationally televised CBC's Doctor Doctor.

Politics

Elections

Fry sought and won the Liberal Party nomination for Vancouver Centre for the 1993 federal election over lawyer David Varty and college lecturer John Lang in March 1993. She was elected to the Canadian House of Commons, defeating Progressive Conservative Prime Minister Kim Campbell. Fry was only the fifth person to unseat a sitting prime minister, and the first to do so on his or her first try for office. Fry has been re-elected in every subsequent election (1997, 2000, 2004, 2006, 2008, and 2011). In 2006, she beat high profile NDP activist and former MP Svend Robinson and in 2008 she defeated high profile Conservative Lorne Mayencourt. Fry was re-elected in 2011 by a margin of approximately 2,000 votes.

In government

She served as Parliamentary Secretary to the Minister of National Health and Welfare from 1993 until 1996 when she was appointed to the Cabinet as Secretary of State for Multiculturalism and Status of Women.

Fry ignited a political backlash when, on March 21, 2001, in reply to a question in the House of Commons, she claimed that crosses were being burned on lawns in Prince George, British Columbia "as we speak". No evidence of this had ever been given and, when asked to justify her claim, she stated that the mayor of Prince George had informed her of this. When asked, the mayor denied having said such a thing. It was later suggested Fry had confused Prince George with Merritt, British Columbia, where a Ku Klux Klan grand wizard was arrested following reported racist activity. Fry was dropped from Cabinet when it was shuffled in 2002.

When Paul Martin became Prime Minister of Canada at the end of 2003, he made her Parliamentary Secretary to the Minister of Citizenship and Immigration with special emphasis on Foreign Credentials. After the 2004 election, she was named Parliamentary Secretary to the Minister of Citizenship and Immigration and the Minister of Human Resources and Skills Development with special emphasis on the Internationally Trained Workers Initiative.

In opposition

When the Liberals lost power in 2006, Fry was named as Critic for Sport Canada in the Liberal shadow cabinet.

On May 4, 2006, Fry became the 11th person, 3rd woman, and the only Westerner to officially enter the Liberal party leadership race. Fry launched her leadership campaign saying that Canada's diversity is its greatest competitive advantage - "our weapon of mass inclusion" - and called for a "non-ideological" approach to problem solving. She withdrew from the contest on September 25 and announced her support for Bob Rae.

Re-elected in Vancouver Centre for a sixth term in 2008, Fry was appointed the Official Opposition Critic for Canadian Heritage. On November 21, 2008, Liberal leadership candidate Bob Rae announced that Fry would serve as his Campaign Co-Chair in British Columbia.

In 2011, as the Liberals lost their designation as Official Opposition, Fry was named Liberal Critic for Health.

References

External links

Official site

Official YouTube Page

How'd They Vote?: Hedy Fry's voting history and quotes

Category:1941 births Category:Living people Category:Members of the House of Commons of Canada from British Columbia Category:Liberal Party of Canada MPs Category:Members of the Queen's Privy Council for Canada Category:Canadian people of Indian descent Category:Trinidad and Tobago people of Indian descent Category:Trinidad and Tobago emigrants to Canada Category:Canadian women Members of Parliament Category:Women in British Columbia politics Category:Alumni of the University of Oxford

fr:Hedy Fry