Rene Descartes came up with the word imaginary in 1637 to describe them. It was a derogatory term. He (and many other mathematicians of that age) did not like imaginary numbers. Many people didn't believe in them, because they were not real.
They were discovered when Cardano solved the third degree equation. In the formulas that arose to solve the third degree equation, Cardano needed to take the square root of negative numbers and add them up in a certain way. The strange thing that happened was that the formulas used these complex numbers, even if the solutions to the equation where all real. This baffled the mathematicians of the time, because how could these strange numbers turn out to be "real"? Later this was considered totally correct, when the field of complex numbers was better undestood.
No because natural numbers are a subset of real numbers
Real numbers are all numbers which do not contain "i", when "i" represents the square root of -1. All numbers which do contain "i" are "imaginary numbers" and are not real numbers. This means that all numbers you'd ordinarily use are real numbers - all the counting numbers (integers) and all decimals are real numbers. So in answer to your question, all the real numbers that are not whole numbers are all the decimal numbers - including irrational decimals such as pi.
yesYes, integers are real numbers.
Probably all mathematicians, from very ancient times.
As an essential component of mathematics, the idea of real numbers is not credited to a single person. Several mathematicians and academics have contributed to the evolution of real numbers over the course of centuries. The concept of real numbers evolved progressively over time, including contributions from the Greeks, Egyptians, and Babylonians among other ancient civilizations. However, during the Renaissance and Enlightenment eras, mathematicians like RenΓ© Descartes, Pierre de Fermat, and Isaac Newton, among others, improved and codified the present understanding of real numbers, including their properties and notation. The introduction of the decimal system by Indian mathematicians in the 9th century was a significant turning point in the evolution of real numbers as it profoundly affected how numbers were represented and understood. for more information visit : webdigitalguru.in
There are mathematical concepts that mathematicians call "imaginary numbers" these are a multiple of the square root of minus 1. Infinity is not a real number either.
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Real numbers are not a single discovery, made at a certain moment by a single person. Check the Wikipedia article on "Real numbers", section "History", for some of the key events related to real numbers.
There is no real number whose square root can be negative so there is no real solution. So mathematicians invented the imaginary number i with the property that i*i = -1 i is fundamental to complex numbers.
In real life one can do very well with nothing but rational numbers. Real numbers that are not rational can be approximated with whatever degree of accuracy is needed, which is exactly what computers and calculators do . Real numbers are essential to mathematical theory but unless you are a mathematician or need to understand higher mathematics in a rigorous way, you can do very well with only a vague , intuitive understanding of real numbers. In fact, it was not until 1870 ,or so, that mathematicians devised a satisfactory definition of real numbers.
The Fibonacci sequence is named after Italian mathematician Leonardo of Pisa, known as Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been described earlier as Virahankanumbers in Indian mathematics.
Rene Descartes came up with the word imaginary in 1637 to describe them. It was a derogatory term. He (and many other mathematicians of that age) did not like imaginary numbers. Many people didn't believe in them, because they were not real.
Mathematics is beautiful in itself. Back in the 1700s and later, mathematicians studied "imaginary" numbers (numbers that involve a factor of the square root of -1) knowing that they didn't describe anything "real", the way "real numbers" do. But when beauty can be melded to practicality, things get REALLY interesting. It turns out that you can use imaginary numbers and "complex numbers" (which have a "real" component and an "imaginary" component) to describe the way radiation and electromagnetic fields behave.
They both considered "identity elements". 0 is actually the identity element under addition for the real numbers, since if a is any real number, a + 0 = 0 + a = a. Mathematicians refers to 0 as the additive identity (or better said, the reflexive identity of addition). 1 is a separate and special entity called 'Unity' or 'Identity element'. 1 is actually the identity element under multiplication for the real numbers, since a x 1 = 1 x a = a. Mathematicians refers to 1 as the multiplicative identity (or better said, the reflex identity of multiplication).