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Q: Why does a real number have to be rational or irrational?

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A real number which is not a rational number is an irrational number.

Real numbers can be rational or irrational because they both form the number line.

It is an integer. All integers are rational but not irrational. All rational and irrational numbers are real numbers.

A real number dosen't have to be a rational number as a real number can be rational or irrational i.e the root of 2 is irrational and real. So is (pi).

An irrational number is a real number that is not rational.

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A real number which is not a rational number is an irrational number.

Real numbers can be rational or irrational because they both form the number line.

It is an integer. All integers are rational but not irrational. All rational and irrational numbers are real numbers.

A real number dosen't have to be a rational number as a real number can be rational or irrational i.e the root of 2 is irrational and real. So is (pi).

An irrational number is a real number that is not rational.

No it cannot. Irrational means "not rational".

Yes it will be. The set of real numbers can be divided into two distinct sets: rational and irrational. So if it is not rational, then it is irrational.

A rational number cannot also be irrational. A real number is either rational, or it is irrational.

The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.

irrational number

Integers are rational. In the set of real numbers, every number is either rational or irrational; a number can't be both or neither.

a real number is a number that can be rational or irrational