Q: Are there any real numbers that are neither rational or irrational?

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No. There are numbers that are beyond real numbers, such as complex numbers which are neither rational nor irrational.

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

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.

All rational and irrational numbers are real numbers.

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

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No. There are numbers that are beyond real numbers, such as complex numbers which are neither rational nor irrational.

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

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.

All rational and irrational numbers are real numbers.

Both irrational and rational are real. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

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.

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

Because irrational numbers are defined as real numbers which are not rational.

Because irrational numbers are defined as all real numbers which are not rational.

No. Real numbers are divided into two DISJOINT (non-overlapping) sets: rational numbers and irrational numbers. A rational number cannot be irrational, and an irrational number cannot be rational.

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

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