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Q: Who is known for his definition of irrational numbers?

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No. Irrational numbers by definition fall into the category of Real Numbers.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

Yes, irrational numbers are never rational numbers because irrational numbers can't be expressed, by definition, as a fraction of two integers.

Yes. The definition of a surd is "an irrational number"

Pi is irrational. Irrational numbers, by definition, have no factors.

An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator.

It is a non-terminating, non-repeating decimal representation. That is a definition of irrational numbers.

The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.

the collection of rational and irrational numbeers is known as real numbers

Because that is the definition of irrational numbers: They are the numbers that cannot be written as a ratio of two integers! A fraction is a ratio of two integers.

Pi and the square root of two are irrational numbers.

All irrational numbers are Real numbers - it's part of the definition of an irrational number. Imaginary numbers are neither rational nor irrational. An example of a number that is both Real and irrational is the square root of two. Another example is the number pi.

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