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What are the real numbers? That's a good question but rather touchy. See this Quora answer.
A real number can be either rational or irrational (not having a certain pattern) & positive, negative or zero. That is the most basic definition of a real number. Real numbers are used to measure continuous data (not discrete/discontinuous).
For more information, here's another link: http://www.mathsisfun.com/numbers/real-numbers.html