how is 1/3 of a set and 1/3 of a whole the same and different
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The set of integers is the same as the set of whole numbers.
Each integer is a whole number and each whole number is an integer. So the set of all integers is the same as the set of all whole numbers. By the equivalence of sets, integers and whole numbers are the same.
The set of whole numbers includes all their additive opposites. So the set is the same as the one you started with.
Yes, but not a proper subset: they are the same set.
Assuming that you mean opposites (rather than oppisites), the answer will depend on what kind of opposites: additive opposites or multiplicative opposites.In the first case you have the same set as you started with: whole numbers.In the second, you will have the set that consists of the union ofall whole numbers,all unit fractions between -1 and +1. But, you have a problem with zero: its multiplicative opposite is not defined.