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This means that they include all the positive and negative numbers, the zero symbol, and the numbers that can not be expressed by fractions of two integers that have non-zero numbers as their denominator.A real number can be expressed in different ways, on the one hand there are real numbers that can be expressed very easily, since they do not have complex rules to do so.
These are the integers and the fractionals, such as number 67 which is an integer, or also the 3 4, which is a fractional number composed of two integers, whose numerator is 3 and its denominator is 4.
However, there are also other numbers that can be expressed under different, more complex mathematical rules, such as numbers whose decimal numbers are infinite, such as the number π or √ 2 and that are used to perform mathematical calculations but can not be represented as a unique numeric symbol.The real numbers are represented by the letter R, and appear by the need to perform more complex calculations since in times such as between the sixteenth and seventeenth century, new figures were needed for technological advances that could no longer be represented by approximate figures or by colloquial expressions for their inaccuracy.
The rigor of the advance of humanity from its tools, made necessary the creation of new mathematical expressions that give greater accuracy to the calculations.Therefore, the set of real numbers was formed from other subsets of numbers that arose from needs in mathematics, such as negative numbers and fractional numbers and decimals.
In Europe, cradle of science in modernity, negative numbers were not used until the late seventeenth century, however, and had been thought many centuries ago by cultures such as Chinese and Hindu.
It was even possible to discard the solutions of calculations that had negative results, because they were considered unreal numbers.The fractional numbers for their part, were used by the Egyptians to solve different problems.