The concept of real numbers was not invented or discovered by any one person or country. Rather, the concept was improved gradually, over the course of several centuries.
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Real numbers have always been around since people started making computation. A precise definition is more modern and can be done in more than one way. Richard Dedekind (1831-1916) might be given the credit for defining real numbers.
They were not invented, they just "are".
All real numbers are finite. Infinity is not a number.All real numbers are finite. Infinity is not a number.All real numbers are finite. Infinity is not a number.All real numbers are finite. Infinity is not a number.
Irrational numbers are real numbers because they are part of the number line.