Unit fractions (those with a numerator of 1), but I suspect you want Integers:
ℤ ⊂ ℚ
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A whole number is not a set of any kind and so cannot be a subset of rational numbers.
Yes, they are.
Counting numbers are a proper subset of whole numbers which are the same as integers which are a proper subset of rational numbers.
true
No, whole numbers are only a small subset of rational numbers.