Hippasus, However Pythagoras could not accept the existence of Irrational Numbers, because he believed that all numbers had perfect values. But he could not disprove Hippasus' "irrational numbers" and so Hippasus was thrown overboard and drowned.
No. For example, 20.5 is irrational; indeed it was one of the first irrational numbers to be discovered.
The Real numbers
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
They were known to the ancient civilisations. Irrational numbers are supposed to have been discovered by Hippassus of Metapontum, a member of the Pythagorean school in ancient Greece (5th Century BC).
Casually, irrational numbers have the decimal digits recurring to infinity, AND there is no regular order in the decimal digits.
NEVER
Pythogora
Possibly 5th Century BC
No. For example, 20.5 is irrational; indeed it was one of the first irrational numbers to be discovered.
Probably the ancient Egyptians who discovered that the diagonal of a unit square was not a rational number. And then discovered other such numbers.
They are irrational numbers!
They are numbers that are infinite
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.
No. Irrational numbers are real numbers, therefore it is not imaginary.
Yes, no irrational numbers are whole numbers.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
No, but the majority of real numbers are irrational. The set of real numbers is made up from the disjoint subsets of rational numbers and irrational numbers.