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.
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Yes.
The subset consisting of the one number, 7.5 : {7.5}
No. Natural numbers are a very small subset of real numbers.
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Yes - in fact the set of all even numbers is a subset of the set of all integers, which is, in turn, a subset of the set of all real numbers.