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The set of integers, the set of rational numbers, the set of real numbers, the set of complex numbers, ...
Negative rational numbers; Negative real numbers; Rational numbers; Real numbers. The number also belongs to the set of complex numbers, quaternions and supersets.
No, it is not.
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There are lots of subsets; some of the ones that are commonly used are: rational numbers; irrational numbers; positive numbers; negative numbers; non-negative numbers; integers; natural numbers. Remember that a subset simply means a set that is contained in another set. It may even be the same set. So the real numbers are a subset of themselves. The number {3} is a subset of the reals. All the examples above are subsets as well. The set {0,1, 2+i, 2-i} is NOT a subset of the real numbers. The real numbers are a subset of the complex numbers.