History of
Integers
START
For a long time, understanding of negative numbers was delayed by the impossibility of having a negative-number amount of a physical object, for example "minus-three apples", and negative solutions to problems were considered "false".
ANCIENT CHINA
Negative numbers were first mentioned in China around 200 BCE.
- The Chinese people used a rod system for calculations with negative numbers. BLACK rods represented negative numbers and RED rods represented positive numbers. (The opposite of how we think about it today.)
- These numbers and calculations were used in economic systems.
- The idea of negative numbers was not fully accepted, or understood beyond their use in economics.
ANCIENT Greek
The ancient Greeks dismissed any solutions to equations that came out negative. They called them "absurd" and "impossible" and completely ignored them. They couldn't see how a negative answer could be meaningful, because it was not possible to have a quantity that was less than nothing . This opinion was passed down to later mathematicians in Europe for more than a thousand years, so very little progress in negative number arithmetic was made for a long time.
Third century C.E.: Diophantus, in his work Arithmetica, referred to the equation 4x + 20 = 0 as absurd, since it would give the solution x = -4. He also said, "a number to be subtracted, multiplied by a number to be subtracted, gives a number to be added."
india
Seventh Century C.E. Negative numbers were used to represent debts and positive numbers represented assets. The brilliant mathematician and astronomer Brahmagupta is said to be the first to write rules for negative numbers. He wrote most of the rules that we still use to work with negative numbers in addition, subtraction, multiplication, and division.
EUROPE
Sixteenth Century C.E.
Michael Stifel (1487 – 1567)
The translation of texts from ancient civilizations that used negative numbers led to their appearance in Europe. The use of negative numbers became popular with ledgers.
German mathematician. He was the first to use the signs + and -.
Gerolamo Cardano (1501 - 1576)
Italian mathematician. He made the first systematic use of negative numbers in Europe.
EUROPE
EUROPE
Nineteenth Century C.E.
Twentieth Century C.E.
Nicolás Bourbaki
Richard Dedekind (1831-1916)
German mathematician. He defined the set of integers
It is not a person, but a group of French mathematicians from the early twentieth century. They represented the set of integers with the letter Z.
Antequera
Nowadays
How are Integers Used in Everyday Life?
The second-year students of the Pedro Espinosa institute are learning to solve problems and operations with integers and to use them to describe situations in everyday life.
Incomplete History of Integers
mariad.porras
Created on October 17, 2024
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Transcript
History of
Integers
START
For a long time, understanding of negative numbers was delayed by the impossibility of having a negative-number amount of a physical object, for example "minus-three apples", and negative solutions to problems were considered "false".
ANCIENT CHINA
Negative numbers were first mentioned in China around 200 BCE.
ANCIENT Greek
The ancient Greeks dismissed any solutions to equations that came out negative. They called them "absurd" and "impossible" and completely ignored them. They couldn't see how a negative answer could be meaningful, because it was not possible to have a quantity that was less than nothing . This opinion was passed down to later mathematicians in Europe for more than a thousand years, so very little progress in negative number arithmetic was made for a long time.
Third century C.E.: Diophantus, in his work Arithmetica, referred to the equation 4x + 20 = 0 as absurd, since it would give the solution x = -4. He also said, "a number to be subtracted, multiplied by a number to be subtracted, gives a number to be added."
india
Seventh Century C.E. Negative numbers were used to represent debts and positive numbers represented assets. The brilliant mathematician and astronomer Brahmagupta is said to be the first to write rules for negative numbers. He wrote most of the rules that we still use to work with negative numbers in addition, subtraction, multiplication, and division.
EUROPE
Sixteenth Century C.E.
Michael Stifel (1487 – 1567)
The translation of texts from ancient civilizations that used negative numbers led to their appearance in Europe. The use of negative numbers became popular with ledgers.
German mathematician. He was the first to use the signs + and -.
Gerolamo Cardano (1501 - 1576)
Italian mathematician. He made the first systematic use of negative numbers in Europe.
EUROPE
EUROPE
Nineteenth Century C.E.
Twentieth Century C.E.
Nicolás Bourbaki
Richard Dedekind (1831-1916)
German mathematician. He defined the set of integers
It is not a person, but a group of French mathematicians from the early twentieth century. They represented the set of integers with the letter Z.
Antequera
Nowadays
How are Integers Used in Everyday Life?
The second-year students of the Pedro Espinosa institute are learning to solve problems and operations with integers and to use them to describe situations in everyday life.