Possibly 5th Century BC
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Probably the ancient Egyptians who discovered that the diagonal of a unit square was not a rational number. And then discovered other such numbers.
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
All irrational numbers are not rational.