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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.