It belongs to any subset which contains it. For example,
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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.
It belongs to any set that contains it: for example, {4.75, -12, pi, sqrt(5), 29}. It belongs to the set of integers which is a proper subset of rational numbers which is a proper subset of real numbers which is a proper subset of complex numbers. So -12 belongs to all the above sets.
To any set that contains it! It belongs to {14}, or {14, sqrt(2), pi, -3/7}, or all whole numbers between 3 and 53, or multiples of 7, or composite numbers, or counting numbers, or integers, or rational numbers, or real numbers, etc.
Sometimes. The number '4' is real and rational. The number 'pi' is real but not rational.
The only real number that is non-terminating and non-repeating is Pi (pie)