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Negative number
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This thermometer is indicating a negative Fahrenheit temperature (−4°F).
In mathematics, a negative number is a real number that is less than zero. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left. If positive represents above sea level, then negative represents below sea level. If positive represents a deposit, negative represents a withdrawal. They are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common sense idea of an opposite is reflected in arithmetic. For example, −(−3) = 3 because the opposite of an opposite is the original thing.
Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). Conversely, a number that is greater than zero is called positive; zero is usually[1] thought of as neither positive nor negative.[2] The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign.
Every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative whole numbers (together with zero) are referred to as integers.
In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers.
Negative numbers appeared for the first time in history in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese Han Dynasty (202 BC – AD 220), but may well contain much older material.[3] Liu Hui (c. 3rd century) established rules for adding and subtracting negative numbers.[4] By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers. Islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients.[5] Western mathematicians accepted the idea of negative numbers by the 17th century. Prior to the concept of negative numbers, mathematicians such as Diophantus considered negative solutions to problems "false" and equations requiring negative solutions were described as absurd.[6]
Contents
[hide]
1 Introduction
1.1 As the result of subtraction
1.2 The number line
1.3 Signed numbers
2 Everyday uses of negative numbers
2.1 Sport
2.2 Science
2.3 Finance
2.4 Other
3 Arithmetic involving negative numbers
3.1 Addition
3.2 Subtraction
3.3 Multiplication
3.4 Division
4 Negation
5 Formal construction of negative integers
5.1 Uniqueness
6 History
7 See also
8 References
8.1 Citations
8.2 Bibliography
9 External links
Introduction[edit]
As the result of subtraction[edit]
Negative numbers can be thought of as resulting from the subtraction of a larger number from a smaller. For example, negative three is the result of subtracting three from zero:
0 − 3 = −3.
In general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers. For example,
5 − 8 = −3
since 8 − 5 = 3.
The number line[edit]
Main article: Number line
The relationship between negative numbers, positive numbers, and zero is often expressed in the form of a number line:
Numbers appearing farther to the right on this line are greater, while numbers appearing farther to the left are less. Thus zero appears in the middle, with the positive numbers to the right and the negative numbers to the left.
Note that a negative number with greater magnitude is considered less. For example, even though (positive) 8 is greater than (positive) 5, written
8 > 5
negative 8 is considered to be less than negative 5:
−8 < −5.
(Because, for example, if you have £-8, a debt of £8, you would have less after adding, say £10, to it than if you have £-5.) It follows that any negative number is less than any positive number, so
−8 < 5 and −5 < 8.
Signed numbers[edit]
Main article: Sign (mathematics)
In the context of negative numbers, a number that is greater than zero is referred to as positive. Thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign. Positive numbers are sometimes written with a plus sign in front, e.g. +3 denotes a positive three.
Because zero is neither positive nor negative, the term nonnegative is sometimes used to refer to a number that is either positive or zero, while nonpositive is used to refer to a number that is either negative or zero. Zero is a neutral number.
Everyday uses of negative numbers[edit]
Sport[edit]
Goal difference in association football and hockey; points difference in rugby football; net run rate in cricket; golf scores relative to par.
Plus-minus differential in ice hockey: the difference in total goals scored for the team (+) and against the team (−) when a particular player is on the ice is the player’s +/− rating. Players can have a negative (+/−) rating.
Run differential in baseball: the run differential is negative if the team allows more runs than they scored.
British football clubs are deducted points if they enter administration, and thus have a negative points total until they have earned at least that many points that season.
Lap (or sector) times in Formula 1 may be given as the difference compared to a previous lap (or sector) (such as the previous record, or the lap just completed by a driver in front), and will be positive if slower and negative if faster.
In some athletics events, such as sprint races, the hurdles, the triple jump and the long jump, the wind assistance is measured and recorded,[7] and is positive for a tailwind and negative for a headwind.[8]
Science[edit]
Temperatures which are colder than 0 °C or 0 °F.[9][10]
Latitudes south of the equator and longitudes west of the prime meridian.
Topographical features of the earth’s surface are given a height above sea level, which can be negative (e.g. The surface elevation of The Dead Sea or Death Valley).
Electrical circuits. When a battery is connected in reverse polarity, the voltage applied is said to be the opposite of its rated voltage. For example, a 6(V) battery connected in reverse applies a voltage of −6(V).
Ions have a positive or negative electrical charge.
Impedance of an AM broadcast tower used in multi-tower directional antenna arrays can have a positive or negative impedance.
Finance[edit]
Bank account balances which are overdrawn.
Refunds to a credit card or debit card are a negative debit.
A company might make a negative annual profit (i.e. a loss).
The annual percentage growth in a country’s GDP might be negative, which is one indicator of being in a recession.[11]
Occasionally, a rate of inflation may be negative (deflation), indicating a fall in average prices.[12]
The daily change in a share price or stock market index, such as the FTSE 100 or the Dow Jones.
A negative number in financing is synonymous with “debt” and “deficit” which are also known as “being in the red”.
Interest rates can be negative,[13][14][15] when the lender is charged to deposit their money.
Other[edit]
The numbering of storeys in a building below the ground floor.
When playing an audio file on a portable media player, such as an iPod, the screen display may show the time remaining as a negative number, which increases up to zero at the same rate as the time already played increases from zero.
Television game shows:
Participants on QI often finish with a negative points score.
Teams on University Challenge have a negative score if their first answers are incorrect and interrupt the question.
Jeopardy! has a negative money score – contestants play for an amount of money and any incorrect answer that costs them more than what they have now can result in a negative score.
The Price Is Right pricing game Buy or Sell, if any money is lost and is more than the amount currently in the bank, it also incurs a negative score.
The change in support for a political party between elections, known as swing.
A politician's approval rating.[16]
In video games, a negative number indicates loss of life, damage, a score penalty, or consumption of a resource, depending on the genre of the simulation.
Employees with flexible working hours may have a negative balance on their timesheet if they’ve worked fewer total hours than contracted to that point. Employees may be able to take more than their annual holiday allowance in a year, and carry forward a negative balance to the next year.
Transposing notes on an electronic keyboard are shown on the display with positive numbers for increases and negative numbers for decreases, e.g. '−1' for one semitone down.
Arithmetic involving negative numbers[edit]
The minus sign "−" signifies the operator for both the binary (two-operand) operation of subtraction (as in y − z) and the unary (one-operand) operation of negation (as in −x, or twice in −(−x)). A special case of unary negation occurs when it operates on a positive number, in which case the result is a negative number (as in −5).
The ambiguity of the "−" symbol does not generally lead to ambiguity in arithmetical expressions, because the order of operations makes only one interpretation or the other possible for each "−". However, it can lead to confusion and be difficult for a person to understand an expression when operator symbols appear adjacent to one another. A solution can be to parenthesize the unary "−" along with its operand.
For example, the expression 7 + −5 may be clearer if written 7 + (−5) (even though they mean exactly the same thing formally). The subtraction expression 7–5 is a different expression that doesn't represent the same operations, but it evaluates to the same result.
Sometimes in elementary schools a number may be prefixed by a superscript minus sign or plus sign to explicitly distinguish negative and positive numbers as in[17]
−2 + −5 gives −7.
Addition[edit]
A visual representation of the addition of positive and negative numbers. Larger balls represent numbers with greater magnitude.
Addition of two negative numbers is very similar to addition of two positive numbers. For example,
(−3) + (−5) = −8.
The idea is that two debts can be combined into a single debt of greater magnitude.
When adding together a mixture of positive and negative numbers, one can think of the negative numbers as positive quantities being subtracted. For example:
8 + (−3) = 8 − 3 = 5 and (−2) + 7 = 7 − 2 = 5.
In the first example, a credit of 8 is combined with a debt of 3, which yields a total credit of 5. If the negative number has greater magnitude, then the result is negative:
(−8) + 3 = 3 − 8 = −5 and 2 + (−7) = 2 − 7 = −5.
Here the credit is less than the debt, so the net result is a debt.
Subtraction[edit]
As discussed above, it is possible for the subtraction of two non-negative numbers to yield a negative answer:
5 − 8 = −3
In general, subtraction of a positive number yields the same result as the addition of a negative number of equal magnitude. Thus
5 − 8 = 5 + (−8) = −3
and
(−3) − 5 = (−3) + (−5) = −8
On the other hand, subtracting a negative number yields the same result as the addition a positive number of equal magnitude. (The idea is that losing a debt is the same thing as gaining a credit.) Thus
3 − (−5) = 3 + 5 = 8
and
(−5) − (−8) = (−5) + 8 = 3.
Multiplication[edit]
When multiplying numbers, the magnitude of the product is always just the product of the two magnitudes. The sign of the product is determined by the following rules:
The product of one positive number and one negative number is negative.
The product of two negative numbers is positive.
Thus
(−2) × 3 = −6
and
(−2) × (−3) = 6.
The reason behind the first example is simple: adding three −2's together yields −6:
(−2) × 3 = (−2) + (−2) + (−2) = −6.
The reasoning behind the second example is more complicated. The idea again is that losing a debt is the same thing as gaining a credit. In this case, losing two debts of three each is the same as gaining a credit of six:
(−2 debts ) × (−3 each) = +6 credit.
The convention that a product of two negative numbers is positive is also necessary for multiplication to follow the distributive law. In this case, we know that
(−2) × (−3) + 2 × (−3) = (−2 + 2) × (−3) = 0 × (−3) = 0.
Since 2 × (−3) = −6, the product (−2) × (−3) must equal 6.
These rules lead to another (equivalent) rule—the sign of any product a × b depends on the sign of a as follows:
if a is positive, then the sign of a × b is the same as the sign of b, and
if a is negative, then the sign of a × b is the opposite of the sign of b.
The justification for why the product of two negative numbers is a positive number can be observed in the analysis of complex numbers.
Division[edit]
The sign rules for division are the same as for multiplication. For example,
8 ÷ (−2) = −4,
(−8) ÷ 2 = −4,
and
(−8) ÷ (−2) = 4.
If dividend and divisor have the same sign, the result is always positive. Another method of dividing negative numbers is that if one of the numbers being divided is a negative, the answer will be negative.
Negation[edit]
Main article: Additive inverse
The negative version of a positive number is referred to as its negation. For example, −3 is the negation of the positive number 3. The sum of a number and its negation is equal to zero:
3 + (−3) = 0.
That is, the negation of a positive number is the additive inverse of the number.
Using algebra, we may write this principle as an algebraic identity:
x + (−x ) = 0.
This identity holds for any positive number x. It can be made to hold for all real numbers by extending the definition of negation to include zero and negative numbers. Specifically:
The negation of 0 is 0, and
The negation of a negative number is the corresponding positive number.
For example, the negation of −3 is +3. In general,
−(−x) = x.
The absolute value of a number is the non-negative number with the same magnitude. For example, the absolute value of −3 and the absolute value of 3 are both equal to 3, and the absolute value of 0 is 0.
Formal construction of negative integers[edit]
See also: Integer § Construction
In a similar manner to rational numbers, we can extend the natural numbers N to the integers Z by defining integers as an ordered pair of natural numbers (a, b). We can extend addition and multiplication to these pairs with the following rules:
(a, b) + (c, d) = (a + c, b + d)
(a, b) × (c, d) = (a × c + b × d, a × d + b × c)
We define an equivalence relation ~ upon these pairs with the following rule:
(a, b) ~ (c, d) if and only if a + d = b + c.
This equivalence relation is compatible with the addition and multiplication defined above, and we may define Z to be the quotient set N²/~, i.e. we identify two pairs (a, b) and (c, d) if they are equivalent in the above sense. Note that Z, equipped with these operations of addition and multiplication, is a ring, and is in fact, the prototypical example of a ring.
We can also define a total order on Z by writing
(a, b) ≤ (c, d) if and only if a + d ≤ b + c.
This will lead to an additive zero of the form (a, a), an additive inverse of (a, b) of the form (b, a), a multiplicative unit of the form (a + 1, a), and a definition of subtraction
(a, b) − (c, d) = (a + d, b + c).
This construction is a special case of the Grothendieck construction.
Uniqueness[edit]
The negative of a number is unique, as is shown by the following proof.
Let x be a number and let y be its negative. Suppose y′ is another negative of x. By an axiom of the real number system
x + y ′ = 0 , {\displaystyle x+y\prime =0,}
x + y = 0. {\displaystyle x+y\,\,=0.}
And so, x + y′ = x + y. Using the law of cancellation for addition, it is seen that y′ = y. Thus y is equal to any other negative of x. That is, y is the unique negative of x.
History[edit]
For a long time, negative solutions to problems were considered "false". In Hellenistic Egypt, the Greek mathematician Diophantus in the 3rd century AD referred to an equation that was equivalent to 4x + 20 = 4 (which has a negative solution) in Arithmetica, saying that the equation was absurd.[18]
Negative numbers appear for the first time in history in the Nine Chapters on the Mathematical Art (Jiu zhang suan-shu), which in its present form dates from the period of the Han Dynasty (202 BC – AD 220), but may well contain much older material.[3] The mathematician Liu Hui (c. 3rd century) established rules for the addition and subtraction of negative numbers. The historian Jean-Claude Martzloff theorized that the importance of duality in Chinese natural philosophy made it easier for the Chinese to accept the idea of negative numbers.[4] The Chinese were able to solve simultaneous equations involving negative numbers. The Nine Chapters used red counting rods to denote positive coefficients and black rods for negative.[4][19] This system is the exact opposite of contemporary printing of positive and negative numbers in the fields of banking, accounting, and commerce, wherein red numbers denote negative values and black numbers signify positive values. Liu Hui writes:
Now there are two opposite kinds of counting rods for gains and losses, let them be called positive and negative. Red counting rods are positive, black counting rods are negative.[4]
The ancient Indian Bakhshali Manuscript carried out calculations with negative numbers, using "+" as a negative sign.[20] The date of the manuscript is uncertain. LV Gurjar dates it no later than the 4th century,[21] Hoernle dates it between the third and fourth centuries, Ayyangar and Pingree dates it to the 8th or 9th centuries,[22] and George Gheverghese Joseph dates it to about AD 400 and no later than the early 7th century,[23]
During the 7th century AD, negative numbers were used in India to represent debts. The Indian mathematician Brahmagupta, in Brahma-Sphuta-Siddhanta (written c. AD 630), discussed the use of negative numbers to produce the general form quadratic formula that remains in use today.[18] He also found negative solutions of quadratic equations and gave rules regarding operations involving negative numbers and zero, such as "A debt cut off from nothingness becomes a credit; a credit cut off from nothingness becomes a debt. " He called positive numbers "fortunes," zero "a cipher," and negative numbers "debts."[24][25]
In the 9th century, Islamic mathematicians were familiar with negative numbers from the works of Indian mathematicians, but the recognition and use of negative numbers during this period remained timid.[5] Al-Khwarizmi in his Al-jabr wa'l-muqabala (from which we get the word "algebra") did not use negative numbers or negative coefficients.[5] But within fifty years, Abu Kamil illustrated the rules of signs for expanding the multiplication ( a ± b ) ( c ± d ) {\displaystyle (a\pm b)(c\pm d)} ,[26] and al-Karaji wrote in his al-Fakhrī that "negative quantities must be counted as terms".[5] In the 10th century, Abū al-Wafā' al-Būzjānī considered debts as negative numbers in A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen.[26]
By the 12th century, al-Karaji's successors were to state the general rules of signs and use them to solve polynomial divisions.[5] As al-Samaw'al writes:
the product of a negative number — al-nāqiṣ — by a positive number — al-zāʾid — is negative, and by a negative number is positive. If we subtract a negative number from a higher negative number, the remainder is their negative difference. The difference remains positive if we subtract a negative number from a lower negative number. If we subtract a negative number from a positive number, the remainder is their positive sum. If we subtract a positive number from an empty power (martaba khāliyya), the remainder is the same negative, and if we subtract a negative number from an empty power, the remainder is the same positive number.[5]
In the 12th century in India, Bhāskara II gave negative roots for quadratic equations but rejected them because they were inappropriate in the context of the problem. He stated that a negative value is "in this case not to be taken, for it is inadequate; people do not approve of negative roots."
European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debits (chapter 13 of Liber Abaci, AD 1202) and later as losses (in Flos).
In the 15th century, Nicolas Chuquet, a Frenchman, used negative numbers as exponents[27] but referred to them as “absurd numbers.”[28] In his 1544 Arithmetica Integra Michael Stifel also dealt with negative numbers, also calling them numeri absurdi.
In 1545, Gerolamo Cardano, in his Ars Magna, provided the first satisfactory treatment of negative numbers in Europe.[18] He did not allow negative numbers in his consideration of cubic equations, so he had to treat, for example, x3 + ax = b separately from x3 = ax + b (with a,b > 0 in both cases). In all, Cardano was driven to the study of thirteen different types of cubic equations, each expressed purely in terms of positive numbers.
In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". He came to the conclusion that negative numbers were nonsensical.[29]
In the 18th century it was common practice to ignore any negative results derived from equations, on the assumption that they were meaningless.[30]
Gottfried Wilhelm Leibniz was the first mathematician to systematically employ negative numbers as part of a coherent mathematical system, the infinitesimal calculus. Calculus made negative numbers necessary and their dismissal as "absurd numbers" quickly faded.[citation needed]
See also[edit]
Signed zero
Additive inverse
History of zero
Integers
Positive and negative parts
Rational numbers
Real numbers
Sign function
Sign (mathematics)
Signed number representations
References[edit]
Citations[edit]
Jump up ^ For exceptions, see signed zero.
Jump up ^ The convention that zero is neither positive nor negative is not universal. For example, in the French convention, zero is considered to be both positive and negative. The French words positif and négatif mean the same as English "positive or zero" and "negative or zero" respectively.
^ Jump up to: a b Struik, page 32–33. "In these matrices we find negative numbers, which appear here for the first time in history."
^ Jump up to: a b c d Luke Hodgkin (2005). A History of Mathematics : From Mesopotamia to Modernity: From Mesopotamia to Modernity. Oxford University Press. p. 88. ISBN 978-0-19-152383-0. Liu is explicit on this; at the point where the Nine Chapters give a detailed and helpful 'Sign Rule'
^ Jump up to: a b c d e f Rashed, R. (1994-06-30). The Development of Arabic Mathematics: Between Arithmetic and Algebra. Springer. pp. 36–37. ISBN 9780792325659.
Jump up ^ Diophantus, Arithmetica.
Jump up ^ BBC website
Jump up ^ Elitefeet
Jump up ^ Forbes, Robert B. (6 January 1975). "Contributions to the Geology of the Bering Sea Basin and Adjacent Regions: Selected Papers from the Symposium on the Geology and Geophysics of the Bering Sea Region, on the Occasion of the Inauguration of the C. T. Elvey Building, University of Alaska, June 26-28, 1970, and from the 2d International Symposium on Arctic Geology Held in San Francisco, February 1-4, 1971". Geological Society of America. p. 194. Retrieved 6 January 2018 – via Google Books.
Jump up ^ Wilks, Daniel S. (6 January 2018). "Statistical Methods in the Atmospheric Sciences". Academic Press. p. 17. Retrieved 6 January 2018 – via Google Books.
Jump up ^ BBC article
Jump up ^ Article in The Independent
Jump up ^ BBC article
Jump up ^ Think negative interest rates can't happen here? Think again
Jump up ^ Swiss National Bank will cut interest rate to minus 0.25%
Jump up ^ Popularity of Miliband and Clegg falls to lowest levels recorded by ICM poll
Jump up ^ Grant P. Wiggins; Jay McTighe (2005). Understanding by design. ACSD Publications. p. 210. ISBN 1-4166-0035-3.
^ Jump up to: a b c Needham, Joseph; Wang, Ling (1995) [1959]. Science and Civilisation in China: Volume 3; Mathematics and the Sciences of the Heavens and the Earth (reprint ed.). Cambridge: Cambridge University Press. p. 90. ISBN 0-521-05801-5. CS1 maint: Multiple names: authors list (link)
Jump up ^ Needham, Joseph; Wang, Ling (1995) [1959]. Science and Civilisation in China: Volume 3; Mathematics and the Sciences of the Heavens and the Earth (reprint ed.). Cambridge: Cambridge University Press. pp. 90–91. ISBN 0-521-05801-5. CS1 maint: Multiple names: authors list (link)
Jump up ^ Teresi, Dick. (2002). Lost Discoveries: The Ancient Roots of Modern Science–from the Babylonians to the Mayas. New York: Simon & Schuster. ISBN 0-684-83718-8. Page 65.
Jump up ^ Pearce, Ian (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Retrieved 2007-07-24.
Jump up ^ Takao Hayashi (2008), Helaine Selin, ed., "Bakhshālī Manuscript", Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, Springer, 1, p. B2, ISBN 9781402045592
Jump up ^ Teresi, Dick. (2002). Lost Discoveries: The Ancient Roots of Modern Science–from the Babylonians to the Mayas. New York: Simon & Schuster. ISBN 0-684-83718-8. Page 65–66.
Jump up ^ Colva M. Roney-Dougal, Lecturer in Pure Mathematics at the University of St Andrews, stated this on the BBC Radio 4 programme "In Our Time," on 9 March 2006.
Jump up ^ Knowledge Transfer and Perceptions of the Passage of Time, ICEE-2002 Keynote Address by Colin Adamson-Macedo. "Referring again to Brahmagupta's great work, all the necessary rules for algebra, including the 'rule of signs', were stipulated, but in a form which used the language and imagery of commerce and the market place. Thus 'dhana' (= fortunes) is used to represent positive numbers, whereas 'rina' (= debts) were negative".
^ Jump up to: a b Mat Rofa Bin Ismail (2008), Helaine Selin, ed., "Algebra in Islamic Mathematics", Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd ed.), Springer, 1, p. 115, ISBN 9781402045592
Jump up ^ Flegg, Graham; Hay, C.; Moss, B. (1985), Nicolas Chuquet, Renaissance Mathematician: a study with extensive translations of Chuquet's mathematical manuscript completed in 1484, D. Reidel Publishing Co., p. 354, ISBN 9789027718723 .
Jump up ^ Famous Problems and Their Mathematicians, Greenwood Publishing Group, 1999, p. 56, ISBN 9781563084461 .
Jump up ^ Maseres, Francis (1758). A dissertation on the use of the negative sign in algebra: containing a demonstration of the rules usually given concerning it; and shewing how quadratic and cubic equations may be explained, without the consideration of negative roots. To which is added, as an appendix, Mr. Machin's Quadrature of the Circle. Quoting from Maseres' work: If any single quantity is marked either with the sign + or the sign − without affecting some other quantity, the mark will have no meaning or significance, thus if it be said that the square of −5, or the product of −5 into −5, is equal to +25, such an assertion must either signify no more than 5 times 5 is equal to 25 without any regard for the signs, or it must be mere nonsense or unintelligible jargon.
Jump up ^ Martinez, Alberto A. (2006). Negative Math: How Mathematical Rules Can Be Positively Bent. Princeton University Press. a history of controversies on negative numbers, mainly from the 1600s until the early 1900s.
Bibliography[edit]
Bourbaki, Nicolas (1998). Elements of the History of Mathematics. Berlin, Heidelberg, and New York: Springer-Verlag. ISBN 3-540-64767-8.
Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications.
External links[edit]
Wikiquote has quotations related to: Negative number
Maseres' biographical information
BBC Radio 4 series "In Our Time," on Negative Numbers, 9 March 2006
Endless Examples & Exercises: Operations with Signed Integers
Math Forum: Ask Dr. Math FAQ: Negative Times a Negative
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Major League Baseball Most Valuable Player Award
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Major League Baseball Most Valuable Player Award (MVP)
The Most Valuable Player award
Given for
Major League Baseball's Regular Season MVP
Country
United States
Presented by
Baseball Writers' Association of America
History
First award
1931
Most recent
José Altuve, American League
Giancarlo Stanton, National League
The Major League Baseball Most Valuable Player Award (MVP) is an annual Major League Baseball (MLB) award given to one outstanding player in the American League and one in the National League. Since 1931, it has been awarded by the Baseball Writers' Association of America (BBWAA). The winners receive the Kenesaw Mountain Landis Memorial Baseball Award, which became the official name of the award in 1944,[1] in honor of the first MLB commissioner, Kenesaw Mountain Landis, who served from 1920 until his death on November 25, 1944.[1][2]
MVP voting takes place before the postseason, but the results are not announced until after the World Series. The BBWAA began by polling three writers in each league city in 1938, reducing that number to two per league city in 1961.[3] The BBWAA does not offer a clear-cut definition of what "most valuable" means, instead leaving the judgment to the individual voters.[4][5]
First basemen, with 34 winners, have won the most MVPs among infielders, followed by second basemen (16), third basemen (15), and shortstops (15). Of the 25 pitchers who have won the award, 15 are right-handed while 10 are left-handed. Walter Johnson, Carl Hubbell, and Hal Newhouser are the only pitchers who have won multiple times, Newhouser winning consecutively in 1944 and 1945.[6][7]
Hank Greenberg, Stan Musial, Alex Rodriguez, and Robin Yount have won at different positions,[6] while Rodriguez is the only player who has won the award with two different teams at two different positions.[8] Barry Bonds has won the most often (seven times) and the most consecutively (2001–04).[9] Jimmie Foxx was the first player to win multiple times;[10] 9 players have won three times, and 19 have won twice.[11] Frank Robinson is the only player to win the award in both the American and National Leagues.
The award's only tie occurred in the National League in 1979, when Keith Hernandez and Willie Stargell received an equal number of points.[6][12] There have been 18 unanimous winners, who received all the first-place votes.[3] The New York Yankees have the most winning players with 22, followed by the St. Louis Cardinals with 17 winners. The award has never been presented to a member of the following three teams: Arizona Diamondbacks, New York Mets, and Tampa Bay Rays. The most recent recipients are José Altuve in the American League and Giancarlo Stanton in the National League.
In recent decades, pitchers have rarely won the award. When Justin Verlander won the AL award in 2011, he became the first pitcher in either league to be named the MVP since Dennis Eckersley in 1992. Verlander also became the first starting pitcher to win this award since Roger Clemens accomplished the feat in 1986.[13] The National League went even longer without an MVP award to a pitcher. After Bob Gibson won in 1968, no pitcher in that league was named MVP until Clayton Kershaw in 2014.[14]
Contents
[hide]
1 Chalmers Award (1911–1914)
2 League Awards (1922–1929)
3 Baseball Writers' Association of America's Most Valuable Player (1931–present)
4 Key
5 See also
6 Notes
7 References
8 External links
Chalmers Award (1911–1914)[edit]
Ty Cobb won the first American League Chalmers Award in 1911 and was at the center of the controversy over the previous season's award.
Before the 1910 season, Hugh Chalmers of Chalmers Automobile announced he would present a Chalmers Model 30 automobile to the player with the highest batting average in Major League Baseball at the end of the season. The 1910 race for best average in the American League was between the Detroit Tigers' widely disliked[3][15][16] Ty Cobb and Nap Lajoie of the Cleveland Indians. On the last day of the season, Lajoie overtook Cobb's batting average with seven bunt hits against the St. Louis Browns. American League President Ban Johnson said a recalculation showed that Cobb had won the race anyway, and Chalmers ended up awarding cars to both players.[3]
The following season, Chalmers created the Chalmers Award. A committee of baseball writers were to convene after the season to determine the "most important and useful player to the club and to the league". Since the award was not as effective at advertising as Chalmers had hoped, it was discontinued after 1914.[3]
Year
American League winner
Team
Position
National League winner
Team
Position
Ref
1911
Cobb Ty !Ty Cobb §
Detroit Tigers OF
Schulte Frank !Frank Schulte
Chicago Cubs OF [17]
1912
Speaker Tris !Tris Speaker
Boston Red Sox OF
Doyle Larry !Larry Doyle
New York Giants !New York Giants 2B [18]
1913
Johnson Walter !Walter Johnson
Washington Senators !Washington Senators RHP
Daubert Jake !Jake Daubert
Brooklyn Dodgers !Brooklyn Dodgers 1B [19]
1914
Collins Eddie !Eddie Collins
Philadelphia Athletics !Philadelphia Athletics 2B
Evers Johnny !Johnny Evers
Boston Braves !Boston Braves 2B [20]
League Awards (1922–1929)[edit]
Babe Ruth was ineligible for the award in his famous 1927 season by the rules of the American League award because he had previously won in 1923.
In 1922 the American League created a new award to honor "the baseball player who is of the greatest all-around service to his club".[21] Winners, voted on by a committee of eight baseball writers chaired by James Crusinberry,[22] received a bronze medal and a cash prize.[23] Voters were required to select one player from each team and player-coaches and prior award winners were ineligible. These incredible flaws resulted in Babe Ruth only winning 1 MVP as the award was dropped after 1928. Under the All-Star Formula, Ruth would have won the MVP in 1920, 1921, 1923, 1925, 1928 and 1930 [citation needed]. The National League award, without these restrictions, lasted from 1924 to 1929.[3]
Year
American League winner
Team
Position
National League winner
Team
Position
Ref
1922
Sisler George !George Sisler
St. Louis Browns !St. Louis Browns 1B
—
-01 !— -01 !— [24]
1923
Ruth Babe !Babe Ruth §
New York Yankees OF
—
-02 !— -02 !— [25]
1924
Johnson Walter !Walter Johnson (2)
Washington Senators !Washington Senators RHP
Vance Dazzy !Dazzy Vance
Brooklyn Robins !Brooklyn Robins RHP [26]
1925
Peckinpaugh Roger !Roger Peckinpaugh
Washington Senators !Washington Senators SS
Hornsby Rogers !Rogers Hornsby
St. Louis Cardinals 2B [27]
1926
Burns George !George Burns
Cleveland Indians 1B
O'Farrell Bob !Bob O'Farrell
St. Louis Cardinals C [28]
1927
Gehrig Lou !Lou Gehrig
New York Yankees 1B
Waner Paul !Paul Waner
Pittsburgh Pirates OF [29]
1928
Cochrane Mickey !Mickey Cochrane
Oakland Athletics !Philadelphia Athletics C
Bottomley Jim !Jim Bottomley
St. Louis Cardinals 1B [30]
1929
—
-01 !— -01 !—
Hornsby Rogers !Rogers Hornsby (2)
Chicago Cubs 2B [31]
Baseball Writers' Association of America's Most Valuable Player (1931–present)[edit]
The BBWAA first awarded the modern MVP after the 1931 season, adopting the format the National League used to distribute its league award. One writer in each city with a team filled out a ten-place ballot, with ten points for the recipient of a first-place vote, nine for a second-place vote, and so on. In 1938, the BBWAA raised the number of voters to three per city and gave 14 points for a first-place vote. The only significant change since then occurred in 1961, when the number of voters was reduced to two per league city.[3]
Jimmie Foxx was the first player to win three MVP awards.
Hall of Famer and 2-time MVP, Hank Greenberg
Jim Konstanty, to date the only National League relief pitcher to be named MVP won it in 1950.
Hall of Famer Willie Mays won the award in 1954 and 1965 with the same team in different cities.
Barry Bonds' seven MVPs are the most for any individual player.
Alex Rodriguez won the award with two different teams at two different positions.
Albert Pujols won the award three times, all at first base with the St. Louis Cardinals.
Miguel Cabrera was the winner of back-to-back AL Awards from 2012-13.
Josh Donaldson won the AL MVP in 2015.
Year
American League winner
Team
Position
National League winner
Team
Position
Ref
1931 Grove, LeftyLefty Grove† Oakland Athletics !Philadelphia Athletics* LHP Frisch, FrankieFrankie Frisch† St. Louis Cardinals* 2B [32]
1932 Foxx, JimmieJimmie Foxx† Oakland Athletics !Philadelphia Athletics 1B Klein Chuck !Chuck Klein† Philadelphia Phillies OF [33]
1933 Foxx Jimmie !Jimmie Foxx† (2) Oakland Athletics !Philadelphia Athletics 1B Hubbell, CarlCarl Hubbell† San Francisco Giants !New York Giants* LHP [34]
1934 Cochrane, MickeyMickey Cochrane† (2) Detroit Tigers* C Dean, DizzyDizzy Dean† St. Louis Cardinals* RHP [35]
1935 Greenberg, HankHank Greenberg†§ Detroit Tigers* 1B Hartnett, GabbyGabby Hartnett† Chicago Cubs* C [36]
1936 Gehrig, LouLou Gehrig† (2) New York Yankees* 1B Hubbell, CarlCarl Hubbell†§ (2) San Francisco Giants !New York Giants* LHP [37]
1937 Gehringer, CharlieCharlie Gehringer† Detroit Tigers 2B Medwick, JoeJoe Medwick† St. Louis Cardinals OF [38]
1938 Foxx, JimmieJimmie Foxx† (3) Boston Red Sox 1B Lombardi, ErnieErnie Lombardi† Cincinnati Reds C [39]
1939 DiMaggio, JoeJoe DiMaggio† New York Yankees* OF Walters, BuckyBucky Walters Cincinnati Reds* RHP [40]
1940 Greenberg, HankHank Greenberg† (2) Detroit Tigers* OF McCormick, FrankFrank McCormick Cincinnati Reds* 1B [41]
1941 DiMaggio, JoeJoe DiMaggio† (2) New York Yankees* OF Camilli, DolphDolph Camilli Los Angeles Dodgers !Brooklyn Dodgers* 1B [42]
1942 Gordon, JoeJoe Gordon† New York Yankees* 2B Cooper, MortMort Cooper St. Louis Cardinals* RHP [43]
1943 Chandler, SpudSpud Chandler New York Yankees* RHP Musial, StanStan Musial† St. Louis Cardinals* OF [44]
1944 Newhouser, HalHal Newhouser† Detroit Tigers LHP Marion, MartyMarty Marion St. Louis Cardinals* SS [45]
1945 Newhouser, HalHal Newhouser† (2) Detroit Tigers* LHP Cavarretta, PhilPhil Cavarretta Chicago Cubs* 1B [46]
1946 Williams, TedTed Williams† Boston Red Sox* OF Musial, StanStan Musial† (2) St. Louis Cardinals* 1B [47]
1947 DiMaggio, JoeJoe DiMaggio† (3) New York Yankees* OF Elliott, BobBob Elliott Atlanta Braves !Boston Braves 3B [48]
1948 Boudreau, LouLou Boudreau† Cleveland Indians* SS Musial, StanStan Musial† (3) St. Louis Cardinals OF [49]
1949 Williams, TedTed Williams† (2) Boston Red Sox OF Robinson, JackieJackie Robinson† Los Angeles Dodgers !Brooklyn Dodgers* 2B [50]
1950 Rizzuto, PhilPhil Rizzuto† New York Yankees* SS Konstanty, JimJim Konstanty Philadelphia Phillies* RHP [51]
1951 Berra, YogiYogi Berra† New York Yankees* C Campanella, RoyRoy Campanella† Los Angeles Dodgers !Brooklyn Dodgers C [52]
1952 Shantz, BobbyBobby Shantz Oakland Athletics !Philadelphia Athletics LHP Sauer, HankHank Sauer Chicago Cubs OF [53]
1953 Rosen, AlAl Rosen§ Cleveland Indians 3B Campanella, RoyRoy Campanella† (2) Los Angeles Dodgers !Brooklyn Dodgers* C [54]
1954 Berra, YogiYogi Berra† (2) New York Yankees C Mays, WillieWillie Mays† San Francisco Giants !New York Giants* OF [55]
1955 Berra, YogiYogi Berra† (3) New York Yankees* C Campanella, RoyRoy Campanella† (3) Los Angeles Dodgers !Brooklyn Dodgers* C [56]
1956 Mantle, MickeyMickey Mantle†§ New York Yankees* OF Newcombe, DonDon Newcombe Los Angeles Dodgers !Brooklyn Dodgers* RHP [57]
1957 Mantle, MickeyMickey Mantle† (2) New York Yankees* OF Aaron, HankHank Aaron† Atlanta Braves !Milwaukee Braves* OF [58]
1958 Jensen, JackieJackie Jensen Boston Red Sox OF Banks, ErnieErnie Banks† Chicago Cubs SS [59]
1959 Fox, NellieNellie Fox† Chicago White Sox* 2B Banks, ErnieErnie Banks† (2) Chicago Cubs SS [60]
1960 Maris, RogerRoger Maris New York Yankees* OF Groat, DickDick Groat Pittsburgh Pirates* SS [61]
1961 Maris, RogerRoger Maris (2) New York Yankees* OF Robinson, FrankFrank Robinson† Cincinnati Reds* OF [62]
1962 Mantle, MickeyMickey Mantle† (3) New York Yankees* OF Wills, MauryMaury Wills Los Angeles Dodgers SS [63]
1963 Howard, ElstonElston Howard New York Yankees* C Koufax, SandySandy Koufax† Los Angeles Dodgers* LHP [64]
1964 Robinson, BrooksBrooks Robinson† Baltimore Orioles 3B Boyer, KenKen Boyer St. Louis Cardinals* 3B [65]
1965 Versalles, ZoiloZoilo Versalles Minnesota Twins* SS Mays, WillieWillie Mays† (2) San Francisco Giants OF [66]
1966 Robinson, FrankFrank Robinson†§ (2) Baltimore Orioles* OF Clemente, RobertoRoberto Clemente† Pittsburgh Pirates OF [67]
1967 Yastrzemski, CarlCarl Yastrzemski† Boston Red Sox* OF Cepeda, OrlandoOrlando Cepeda†§ St. Louis Cardinals* 1B [68]
1968 McLain, DennyDenny McLain§ Detroit Tigers* RHP Gibson, BobBob Gibson† St. Louis Cardinals* RHP [69]
1969 Killebrew, HarmonHarmon Killebrew† Minnesota Twins 3B McCovey, WillieWillie McCovey† San Francisco Giants 1B [70]
1970 Powell, BoogBoog Powell Baltimore Orioles* 1B Bench, JohnnyJohnny Bench† Cincinnati Reds* C [71]
1971 Blue, VidaVida Blue Oakland Athletics LHP Torre, JoeJoe Torre†[c] St. Louis Cardinals 3B [72]
1972 Allen, DickDick Allen Chicago White Sox 1B Bench, JohnnyJohnny Bench† (2) Cincinnati Reds* C [73]
1973 Jackson, ReggieReggie Jackson†§ Oakland Athletics* OF Rose, PetePete Rose Cincinnati Reds OF [74]
1974 Burroughs, JeffJeff Burroughs Texas Rangers OF Garvey, SteveSteve Garvey Los Angeles Dodgers* 1B [75]
1975 Lynn, FredFred Lynn Boston Red Sox* OF Morgan, JoeJoe Morgan† Cincinnati Reds* 2B [76]
1976 Munson, ThurmanThurman Munson New York Yankees* C Morgan, JoeJoe Morgan† (2) Cincinnati Reds* 2B [77]
1977 Carew, RodRod Carew† Minnesota Twins 1B Foster, GeorgeGeorge Foster Cincinnati Reds OF [78]
1978 Rice, JimJim Rice† Boston Red Sox OF Parker, DaveDave Parker Pittsburgh Pirates OF [79]
1979 Baylor, DonDon Baylor Los Angeles Angels !California Angels LF/DH [80] Hernandez, KeithKeith Hernandez[d] St. Louis Cardinals 1B [12]
Stargell, WillieWillie Stargell†[d] Pittsburgh Pirates* 1B
1980 Brett, GeorgeGeorge Brett† Kansas City Royals* 3B Schmidt, MikeMike Schmidt†§ Philadelphia Phillies* 3B [81]
1981 Fingers, RollieRollie Fingers† Milwaukee Brewers RHP Schmidt, MikeMike Schmidt† (2) Philadelphia Phillies 3B [82]
1982 Yount, RobinRobin Yount† Milwaukee Brewers* SS Murphy, DaleDale Murphy Atlanta Braves OF [83]
1983 Ripken, Jr., CalCal Ripken, Jr.† Baltimore Orioles* SS Murphy, DaleDale Murphy (2) Atlanta Braves OF [84]
1984 Hernandez, WillieWillie Hernández Detroit Tigers* LHP Sandberg, RyneRyne Sandberg† Chicago Cubs 2B [85]
1985 Mattingly, DonDon Mattingly New York Yankees 1B McGee, WillieWillie McGee St. Louis Cardinals* OF [86]
1986 Clemens, RogerRoger Clemens Boston Red Sox* RHP Schmidt, MikeMike Schmidt† (3) Philadelphia Phillies 3B [87]
1987 Bell, GeorgeGeorge Bell Toronto Blue Jays OF Dawson, AndreAndre Dawson† Chicago Cubs OF [88]
1988 Canseco, JoseJose Canseco§ Oakland Athletics* OF Gibson, KirkKirk Gibson Los Angeles Dodgers* OF [89]
1989 Yount, RobinRobin Yount† (2) Milwaukee Brewers OF Mitchell, KevinKevin Mitchell San Francisco Giants* OF [90]
1990 Henderson, RickeyRickey Henderson† Oakland Athletics* OF Bonds, BarryBarry Bonds Pittsburgh Pirates OF [91]
1991 Ripken, Jr., CalCal Ripken, Jr.† (2) Baltimore Orioles SS Pendleton, TerryTerry Pendleton Atlanta Braves* 3B [92]
1992 Eckersley, DennisDennis Eckersley† Oakland Athletics RHP Bonds, BarryBarry Bonds (2) Pittsburgh Pirates OF [93]
1993 Thomas, FrankFrank Thomas†§ Chicago White Sox 1B Bonds, BarryBarry Bonds (3) San Francisco Giants OF [94]
1994 Thomas, FrankFrank Thomas† (2) Chicago White Sox 1B Bagwell, JeffJeff Bagwell†§ Houston Astros 1B [95]
1995 Vaughn, MoMo Vaughn Boston Red Sox 1B Larkin, BarryBarry Larkin† Cincinnati Reds SS [96]
1996 Gonzalez, JuanJuan González Texas Rangers OF Caminiti, KenKen Caminiti§ San Diego Padres 3B [97]
1997 Griffey, Jr., KenKen Griffey, Jr.†§ Seattle Mariners OF Walker, LarryLarry Walker Colorado Rockies OF [98]
1998 Gonzalez, JuanJuan González (2) Texas Rangers OF Sosa, SammySammy Sosa Chicago Cubs OF [99]
1999 Rodriguez, IvanIván Rodríguez† Texas Rangers C Jones, ChipperChipper Jones† Atlanta Braves* 3B [100]
2000 Giambi, JasonJason Giambi Oakland Athletics 1B Kent, JeffJeff Kent San Francisco Giants 2B [101]
2001 Suzuki, IchiroIchiro Suzuki Seattle Mariners OF Bonds, BarryBarry Bonds (4) San Francisco Giants OF [102][103]
2002 Tejada, MiguelMiguel Tejada Oakland Athletics SS Bonds, BarryBarry Bonds§ (5) San Francisco Giants* OF [104]
2003 Rodriguez, AlexAlex Rodriguez Texas Rangers SS Bonds, BarryBarry Bonds (6) San Francisco Giants OF [105]
2004 Guerrero, VladimirVladimir Guerrero† Los Angeles Angels !Anaheim Angels OF Bonds, BarryBarry Bonds (7) San Francisco Giants OF [106]
2005 Rodriguez, AlexAlex Rodriguez (2) New York Yankees 3B Pujols, AlbertAlbert Pujols^ St. Louis Cardinals 1B [107]
2006 Morneau, JustinJustin Morneau Minnesota Twins 1B Howard, RyanRyan Howard^ Philadelphia Phillies 1B [108]
2007 Rodriguez, AlexAlex Rodriguez (3) New York Yankees 3B Rollins, JimmyJimmy Rollins Philadelphia Phillies SS [109]
2008 Pedroia, DustinDustin Pedroia^ Boston Red Sox 2B Pujols, AlbertAlbert Pujols^ (2) St. Louis Cardinals 1B [110]
2009 Mauer, JoeJoe Mauer^ Minnesota Twins C Pujols, AlbertAlbert Pujols^§ (3) St. Louis Cardinals 1B [103][111]
2010 Hamilton, JoshJosh Hamilton^ Texas Rangers* OF Votto, JoeyJoey Votto^ Cincinnati Reds 1B [112][113]
2011 Verlander, JustinJustin Verlander^ Detroit Tigers RHP Braun, RyanRyan Braun^ Milwaukee Brewers OF [114][115]
2012 Cabrera, MiguelMiguel Cabrera^ Detroit Tigers* 3B Posey, BusterBuster Posey^ San Francisco Giants* C [116][117]
2013 Cabrera, MiguelMiguel Cabrera^ (2) Detroit Tigers 3B McCutchen, AndrewAndrew McCutchen^ Pittsburgh Pirates OF [118][119]
2014 Trout, MikeMike Trout^§ Los Angeles Angels of Anaheim OF Kershaw, ClaytonClayton Kershaw^ Los Angeles Dodgers LHP [14][120]
2015 Donaldson, JoshJosh Donaldson^ Toronto Blue Jays 3B Harper, BryceBryce Harper^§ Washington Nationals OF [121][122]
2016 Trout, MikeMike Trout^ (2) Los Angeles Angels of Anaheim OF Bryant, KrisKris Bryant^ Chicago Cubs* 3B/OF [123]
2017 Altuve, JoséJosé Altuve^ Houston Astros* 2B Stanton, GiancarloGiancarlo Stanton^ Miami Marlins OF [123]
Key[edit]
Year
Links to the article about the corresponding Major League Baseball season
Member of the National Baseball Hall of Fame as a player[124][125]
^
Denotes player who is still active[a]
§
Unanimous selection[b][3]
Player (X)
Denotes winning player and number of times they had won the award at that point
*
Team won League Pennant
P
Pitcher (RHP indicates right-handed; LHP indicates left-handed)
C
Catcher
1B
First baseman
2B
Second baseman
3B
Third baseman
SS
Shortstop
OF
Outfielder
DH
Designated hitter
See also[edit]
"Esurance MLB Awards" Best Major Leaguer (in MLB; all positions) (there are also Best Hitter and Best Pitcher awards (in MLB))
"Players Choice Awards" Player of the Year (in MLB; all positions) (there are also Outstanding Player and Outstanding Pitcher awards (in each league))
Baseball America Major League Player of the Year (in MLB; all positions)
Baseball Digest Player of the Year (in MLB; position players only; from 1969 to 1993, included all positions; in 1994, a separate Pitcher of the Year award was added)
Best Major League Baseball Player ESPY Award (in MLB; all positions)
The Sporting News Most Valuable Player Award (in each league) (discontinued in 1946)
Sporting News Player of the Year (in MLB; position players only)
List of Major League Baseball awards
Baseball awards
Notes[edit]
a A player is considered inactive if he has announced his retirement or not played for a full season.
b A unanimous victory indicates that the player received all possible first-place votes.
c Torre is a member of the Hall of Fame, but not as a player. He was inducted in 2014 as a manager.[126]
d Hernandez and Stargell both received 216 points in the 1979 voting.[12]
References[edit]
^ Jump up to: a b "Landis, Kenesaw". National Baseball Hall of Fame and Museum. Archived from the original on 2011-11-22. Retrieved 2011-11-22.
Jump up ^ Gillette, Gary; Palmer, Pete (2007). The ESPN Baseball Encyclopedia (Fourth ed.). New York: Sterling Publishing Co. p. 1763. ISBN 978-1-4027-4771-7.
^ Jump up to: a b c d e f g h Gillette & Palmer, pp. 1764–1765
Jump up ^ Kepner, Tyler (September 4, 2011). "Where Do You Find Value? Discussing the M.V.P. Criteria". The New York Times. p. SP3. Archived from the original on October 27, 2014. Retrieved September 6, 2011.
Jump up ^ For the definition that appears on the BBWAA ballot (including pitchers and designated hitters), go to Voting FAQ and scroll down. Baseball Writers' Association of America. Retrieved November 7, 2016.
^ Jump up to: a b c "Major League Baseball's Most Valuable Player Award Winners". Baseball Digest. Evanston, Illinois: Century Publishing Co. 59 (12): 86–89. December 2000. ISSN 0005-609X. Retrieved December 29, 2009.
Jump up ^ "Walter Johnson Statistics and History". Baseball-Reference.com. Archived from the original on 2018-05-07. Retrieved 2016-01-23.
Jump up ^ "Alex Rodriguez Statistics". Baseball-Reference.com. Archived from the original on July 12, 2010. Retrieved December 3, 2009.
Jump up ^ "Barry Bonds Statistics". Baseball-Reference.com. Archived from the original on July 3, 2011. Retrieved December 3, 2009.
Jump up ^ "Jimmie Foxx Statistics". Baseball-Reference.com. Archived from the original on April 12, 2009. Retrieved December 3, 2009.
Jump up ^ "Most Valuable Player MVP Awards & Cy Young Awards Winners". Baseball-Reference.com. Archived from the original on January 9, 2010. Retrieved December 3, 2009.
^ Jump up to: a b c "Baseball Awards Voting for 1979". Baseball-Reference.com. Archived from the original on March 30, 2009. Retrieved December 28, 2009.
Jump up ^ Kepner, Tyler (November 21, 2011). "Verlander Is First Pitcher Named M.V.P. Since 1992". The New York Times. Archived from the original on March 19, 2018.
^ Jump up to: a b "Clayton Kershaw, Dodgers". Baseball Writers' Association of America. Retrieved January 19, 2015.
Jump up ^ Doyle, Havey (July 4, 1941). "Mirrors of Sport". Pittsburgh Post-Gazette. p. 18. Retrieved January 19, 2010. [dead link]
Jump up ^ Schwartz, Larry. "He was a pain ... but a great pain". ESPN.com. Archived from the original on October 3, 2009. Retrieved January 19, 2010.
Jump up ^ "Baseball Awards Voting for 1911". Baseball-Reference.com. Archived from the original on February 10, 2009. Retrieved December 3, 2009.
Jump up ^ "Baseball Awards Voting for 1912". Baseball-Reference.com. Archived from the original on January 30, 2009. Retrieved December 3, 2009.
Jump up ^ "Baseball Awards Voting for 1913". Baseball-Reference.com. Archived from the original on January 29, 2009. Retrieved December 3, 2009.
Jump up ^ "Baseball Awards Voting for 1914". Baseball-Reference.com. Archived from the original on January 30, 2009. Retrieved December 3, 2009.
Jump up ^ Newman, Mark (November 14, 2009). "One of a kind: Another MVP for A-Rod". MLB.com. Retrieved December 5, 2009.
Jump up ^ Gould, Alan (December 8, 1929). "Rogers Hornsby Voted Most Valuable Player in National League". Reading Eagle. Retrieved January 6, 2010.
Jump up ^ "Player Award Goes to Hornsby again". The New York Times. December 8, 1929. p. S2.
Jump up ^ "Baseball Awards Voting for 1922". Baseball-Reference.com. Archived from the original on February 16, 2009. Retrieved December 5, 2009.
Jump up ^ "Baseball Awards Voting for 1923". Baseball-Reference.com. Archived from the original on February 8, 2009. Retrieved December 5, 2009.
Jump up ^ "Baseball Awards Voting for 1924". Baseball-Reference.com. Archived from the original on February 16, 2009. Retrieved December 5, 2009.
Jump up ^ "Baseball Awards Voting for 1925". Baseball-Reference.com. Archived from the original on February 16, 2009. Retrieved December 8, 2009.
Jump up ^ "Baseball Awards Voting for 1926". Baseball-Reference.com. Archived from the original on February 16, 2009. Retrieved December 8, 2009.
Jump up ^ "Baseball Awards Voting for 1927". Baseball-Reference.com. Archived from the original on February 16, 2009. Retrieved December 8, 2009.
Jump up ^ "Baseball Awards Voting for 1928". Baseball-Reference.com. Archived from the original on January 5, 2010. Retrieved December 8, 2009.
Jump up ^ "Baseball Awards Voting for 1929". Baseball-Reference.com. Archived from the original on March 29, 2009. Retrieved December 8, 2009.
Jump up ^ "Baseball Awards Voting for 1931". Baseball-Reference.com. Archived from the original on March 4, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1932". Baseball-Reference.com. Archived from the original on January 5, 2010. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1933". Baseball-Reference.com. Archived from the original on September 18, 2011. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1934". Baseball-Reference.com. Archived from the original on May 22, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1935". Baseball-Reference.com. Archived from the original on February 12, 2010. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1936". Baseball-Reference.com. Archived from the original on September 16, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1937". Baseball-Reference.com. Archived from the original on June 21, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1938". Baseball-Reference.com. Archived from the original on February 9, 2010. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1939". Baseball-Reference.com. Archived from the original on February 2, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1940". Baseball-Reference.com. Archived from the original on February 12, 2010. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1941". Baseball-Reference.com. Archived from the original on February 1, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1942". Baseball-Reference.com. Archived from the original on February 1, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1943". Baseball-Reference.com. Archived from the original on February 23, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1944". Baseball-Reference.com. Archived from the original on February 10, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1945". Baseball-Reference.com. Archived from the original on April 13, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1946". Baseball-Reference.com. Archived from the original on February 23, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1947". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1948". Baseball-Reference.com. Archived from the original on February 23, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1949". Baseball-Reference.com. Archived from the original on February 23, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1950". Baseball-Reference.com. Archived from the original on February 23, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1951". Baseball-Reference.com. Archived from the original on February 28, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1952". Baseball-Reference.com. Archived from the original on March 29, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1953". Baseball-Reference.com. Archived from the original on February 28, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1954". Baseball-Reference.com. Archived from the original on August 7, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1955". Baseball-Reference.com. Archived from the original on March 6, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1956". Baseball-Reference.com. Archived from the original on February 10, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1957". Baseball-Reference.com. Archived from the original on February 22, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1958". Baseball-Reference.com. Archived from the original on August 7, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1959". Baseball-Reference.com. Archived from the original on April 11, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1960". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1961". Baseball-Reference.com. Archived from the original on February 14, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1962". Baseball-Reference.com. Archived from the original on February 10, 2009. Retrieved December 11, 2009.
Jump up ^ "Baseball Awards Voting for 1963". Baseball-Reference.com. Archived from the original on February 14, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1964". Baseball-Reference.com. Archived from the original on March 30, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1965". Baseball-Reference.com. Archived from the original on March 30, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1966". Baseball-Reference.com. Archived from the original on February 23, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1967". Baseball-Reference.com. Archived from the original on February 12, 2010. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1968". Baseball-Reference.com. Archived from the original on March 30, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1969". Baseball-Reference.com. Archived from the original on February 1, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1970". Baseball-Reference.com. Archived from the original on February 22, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1971". Baseball-Reference.com. Archived from the original on March 30, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1972". Baseball-Reference.com. Archived from the original on August 31, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1973". Baseball-Reference.com. Archived from the original on February 28, 2009. Retrieved December 12, 2009.
Jump up ^ "Baseball Awards Voting for 1974". Baseball-Reference.com. Archived from the original on March 6, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1975". Baseball-Reference.com. Archived from the original on April 21, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1976". Baseball-Reference.com. Archived from the original on March 29, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1977". Baseball-Reference.com. Archived from the original on February 12, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1978". Baseball-Reference.com. Archived from the original on February 28, 2009. Retrieved December 28, 2009.
Jump up ^ "Don Baylor 1979 Batting Splits - Baseball-Reference.com". Baseball-Reference.com. Archived from the original on 18 October 2017. Retrieved 7 May 2018.
Jump up ^ "Baseball Awards Voting for 1980". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1981". Baseball-Reference.com. Archived from the original on February 10, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1982". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1983". Baseball-Reference.com. Archived from the original on March 30, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1984". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1985". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1986". Baseball-Reference.com. Archived from the original on April 15, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1987". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1988". Baseball-Reference.com. Archived from the original on March 28, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1989". Baseball-Reference.com. Archived from the original on February 23, 2011. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1990". Baseball-Reference.com. Archived from the original on April 15, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1991". Baseball-Reference.com. Archived from the original on April 10, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1992". Baseball-Reference.com. Archived from the original on April 6, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1993". Baseball-Reference.com. Archived from the original on April 14, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1994". Baseball-Reference.com. Archived from the original on May 9, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1995". Baseball-Reference.com. Archived from the original on April 18, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1996". Baseball-Reference.com. Archived from the original on February 23, 2011. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1997". Baseball-Reference.com. Archived from the original on April 9, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1998". Baseball-Reference.com. Archived from the original on April 14, 2008. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 1999". Baseball-Reference.com. Archived from the original on February 23, 2011. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2000". Baseball-Reference.com. Archived from the original on August 31, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2001". Baseball-Reference.com. Archived from the original on February 10, 2009. Retrieved December 28, 2009.
^ Jump up to: a b "Albert Pujols of St. Louis Cardinals is unanimous National League MVP". ESPN. The Associated Press. November 25, 2009. Archived from the original on February 9, 2010. Retrieved July 14, 2010.
Jump up ^ "Baseball Awards Voting for 2002". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2003". Baseball-Reference.com. Archived from the original on February 23, 2011. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2004". Baseball-Reference.com. Archived from the original on January 9, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2005". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2006". Baseball-Reference.com. Archived from the original on February 14, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2007". Baseball-Reference.com. Archived from the original on February 18, 2009. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2008". Baseball-Reference.com. Archived from the original on January 5, 2010. Retrieved December 28, 2009.
Jump up ^ "Baseball Awards Voting for 2009". Baseball-Reference.com. Archived from the original on November 22, 2009. Retrieved December 3, 2009.
Jump up ^ "Rangers Outfielder Josh Hamilton Honored". Baseball Writers' Association of America. Archived from the original on July 7, 2012. Retrieved November 23, 2010.
Jump up ^ "Reds' Joey Votto Runs Away With Award". Baseball Writers' Association of America. Archived from the original on July 1, 2012. Retrieved November 22, 2010.
Jump up ^ "Justin Verlander Completes Rare Double, Adding MVP to Cy Young". Baseball Writers' Association of America. Archived from the original on July 10, 2012. Retrieved November 21, 2011.
Jump up ^ "Ryan Braun Slugs His Way to Award". Baseball Writers' Association of America. Archived from the original on July 1, 2012. Retrieved November 22, 2011.
Jump up ^ "Mike Trout Highest WAR at Youngest Age". Baseball Writers' Association of America. Archived from the original on July 10, 2012. Retrieved November 15, 2012.
Jump up ^ "YadierMolina". Baseball Writers' Association of America. Retrieved March 13, 2013.
Jump up ^ "Miguel Cabrera Goes Back-to-Back". Baseball Writers' Association of America. Retrieved November 14, 2013.
Jump up ^ "Andrew McCutchen Wins Pirates' 1st MVP since 1992". Baseball Writers' Association of America. Retrieved November 14, 2013.
Jump up ^ "Mike Trout, Angels". Baseball Writers' Association of America. Retrieved January 19, 2015.
Jump up ^ "Josh Donaldson, Blue Jays". Baseball Writer's Association of America. Retrieved November 7, 2016.
Jump up ^ "Bryce Harper, Nationals". Baseball Writers' Association of America. Retrieved November 7, 2016.
^ Jump up to: a b "Angels' Mike Trout wins second AL MVP, outpoints Red Sox's Mookie Betts". usatoday.com. Archived from the original on 17 November 2017. Retrieved 7 May 2018.
Jump up ^ Gillette & Palmer, pp. 1755–1760
Jump up ^ "Baseball Hall of Fame Inductees". Baseball-Reference.com. Archived from the original on January 4, 2010. Retrieved December 3, 2009.
Jump up ^ "Joe Torre". National Baseball Hall of Fame and Museum. Archived from the original on November 15, 2014. Retrieved November 13, 2014.
External links[edit]
Most Valuable Player MVP Awards & Cy Young Awards Winners (1911–present) (and "Multiple Winners of the MVP and Cy Young Awards"). Baseball-Reference.com. Retrieved 2016-11-07.
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American League MVP Award
1931: Grove
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1940: Greenberg
1941: DiMaggio
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1946: Williams
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1970: Powell
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1972: Allen
1973: Jackson
1974: Burroughs
1975: Lynn
1976: Munson
1977: Carew
1978: Rice
1979: Baylor
1980: Brett
1981: Fingers
1982: Yount
1983: Ripken Jr.
1984: Hernández
1985: Mattingly
1986: Clemens
1987: Bell
1988: Canseco
1989: Yount
1990: Henderson
1991: Ripken Jr.
1992: Eckersley
1993: Thomas
1994: Thomas
1995: Vaughn
1996: González
1997: Griffey Jr.
1998: González
1999: I. Rodríguez
2000: Giambi
2001: Suzuki
2002: Tejada
2003: A. Rodriguez
2004: Guerrero
2005: A. Rodriguez
2006: Morneau
2007: A. Rodriguez
2008: Pedroia
2009: Mauer
2010: Hamilton
2011: Verlander
2012: Cabrera
2013: Cabrera
2014: Trout
2015: Donaldson
2016: Trout
2017: Altuve
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National League MVP Award
1931: Frisch
1932: Klein
1933: Hubbell
1934: Dean
1935: Hartnett
1936: Hubbell
1937: Medwick
1938: Lombardi
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1940: McCormick
1941: Camilli
1942: Cooper
1943: Musial
1944: Marion
1945: Cavarretta
1946: Musial
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1948: Musial
1949: J. Robinson
1950: Konstanty
1951: Campanella
1952: Sauer
1953: Campanella
1954: Mays
1955: Campanella
1956: Newcombe
1957: Aaron
1958: Banks
1959: Banks
1960: Groat
1961: F. Robinson
1962: Wills
1963: Koufax
1964: Boyer
1965: Mays
1966: Clemente
1967: Cepeda
1968: B. Gibson
1969: McCovey
1970: Bench
1971: Torre
1972: Bench
1973: Rose
1974: Garvey
1975: Morgan
1976: Morgan
1977: Foster
1978: Parker
1979: Hernandez & Stargell
1980: Schmidt
1981: Schmidt
1982: Murphy
1983: Murphy
1984: Sandberg
1985: McGee
1986: Schmidt
1987: Dawson
1988: K. Gibson
1989: Mitchell
1990: Bonds
1991: Pendleton
1992: Bonds
1993: Bonds
1994: Bagwell
1995: Larkin
1996: Caminiti
1997: Walker
1998: Sosa
1999: Jones
2000: Kent
2001: Bonds
2002: Bonds
2003: Bonds
2004: Bonds
2005: Pujols
2006: Howard
2007: Rollins
2008: Pujols
2009: Pujols
2010: Votto
2011: Braun
2012: Posey
2013: McCutchen
2014: Kershaw
2015: Harper
2016: Bryant
2017: Stanton
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values: Baseball America Major League Player of the Year

values: Best Major League Baseball Player ESPY Award

values: The Sporting News Most Valuable Player Award

values: The Sporting News Player of the Year Award

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Warren Giles Trophy

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William Harridge Trophy

values: Major League Baseball Manager of the Year Award

values: Major League Baseball Rookie of the Year Award

values: Major League Baseball All-Star Game Most Valuable Player Award

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values: MVP de las Grandes Ligas de Béisbol – Spanish

values: Joueur par excellence (Ligue majeure de baseball) – French

values: 메이저 리그 베이스볼 최우수 선수상 – Korean

values: Major League Baseball Most Valuable Player Award – Italian

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values: Major League Baseball Most Valuable Player Award – Polish

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values: Major League Baseball Most Valuable Player Award – Simple English

values: Найцінніший гравець Головної бейсбольної ліги – Ukrainian

values: 美國職棒大聯盟最有價值球員獎 – Chinese

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