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No. There are several real numbers that are not rational (e.g. pi). However, every rational number is also a real number.

In general, whole numbers/natural numbers is a subset of the integers (i.e. every whole number is an integer), the integers is a subset of the rationals, the rationals are a subset of the real numbers.

I think the real numbers are a subset of the complex numbers, but I'm not 100% positive on that.

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