All Irrational Numbers, complex number and so on.
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No, it is not.
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
The Real numbers
It is the rational numbers.
No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.