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Yes it is. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
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.
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).
There are infinitely many rational numbers between any two rational numbers. And the cardinality of irrational numbers between any two rational numbers is even greater.
When added to a rational number, any irrational number will produce an irrational number.also, when added to an irrational number, any rational number will produce an irrational number.