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It has been known from very ancient times that the length of the diagonal of a unit square is not a rational number. There were no specific mathematicians who "discovered" real numbers. Furthermore, all mathematicians of any significance, contributed to our understanding of real numbers.
Probably all mathematicians, from very ancient times.
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.
"http://wiki.answers.com/Q/Who_were_the_Mathematicians_in_the_field_of_real_numbers_and_polynomials_write_about_them"
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.
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.
Real numbers.
There is only one set of Real numbers.
The only thing I can think of that you might mean is an imaginary or complex number. Since there is no solution to √(-1) mathematicians labeled it as i which is the imaginary number, and any number that includes purely i is also imaginary. Complex numbers are a mix of both real and imaginary numbers. for example 3 is real, 5i is imaginary and 3+5i is complex. Hopefully this answers what you meant.
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.
In the context of real numbers, only the number 0.