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Q: Is the difference of any two irrational numbers rational or irrational?

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Any rational or irrational is real. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

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

In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.

In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.

The sum or the difference between two irrational numbers could either be rational or irrational, however, it should be a real number.

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

Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).

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.

There isn't any. If there were, then the intersection would consist of all the numbers that are both rational and irrational, and there aren't any of those.

Any number is NOT rational. In fact, there are more irrational numbers than there are rational.

Any rational or irrational numbers are called real numbers.

Infinitely many. In fact, between any two different real numbers, there are infinitely many rational numbers, and infinitely many irrational numbers. (More precisely, beth-zero rational numbers, and beth-one irrational numbers - that is, there are more irrational numbers than rational numbers in any such interval.)

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