History of negative numbers
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Early writings of the Babylonians, Hindus, Egyptian, or Chinese do not contain any trace of the recognition of negative numbers
Nonetheless, they had no problems doing correctly computations involving subtractions such as:
(6 − 4) × (4 − 3) or (8 − 8) × (7 − 5)
The first mentioned of negative numbers can be traced to the Chinese in 200 B.C.E.
The Chinese used red rods to represent positive numbers, but black rods to represent negative numbers
In the fourth century, the Alexandrian mathematician Diophantus said in his text Arithmetica that the following equation is absurd
4x + 20 = 4
He said this because x would have to be -4
In India, negative numbers started appearing around (A.D. 620-630) in the work of the Hindu Brahmagupta
He called positive numbers affirmative quantities. For instance, he said in his work that the sum of two
affirmative quantities is affirmative.
This means that the sum of two positive numbers is positive
Around 1300, Chinese mathematician Chu Shi-Ku gave the "rule of sign"
In the 16th century, around 1545, the study of solutions of equations began in Italy.
This led the Italian mathematician
Cardano to recognize negative roots as he tried to understand the meaning of the square root of a negative number such as
During that time, he also clearly stated rules of negative
There has been various notations to represent negative numbers
The Hindus put a small circle or dot over or next to a number to denote that it was negative
The Chinese drew a slash through a portion of the number to indicate that the number negative
For example, -1020 was written as shown below. Here, the slash is drawn over two bars or the number 2
Cardano used the symbol m: for negative numbers. For examples, -6 can be written as m:6
Other popular topics related to integers are modeling integers with chips
and integers and inductive reasoning
For more information on the history of negative number check,
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