All numbers have opposites that are the same as their absolute values.
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The absolute value of the answer is the difference between the absolute values of the two numbers and the sign associated with it is the same as that of the number with the greater absolute value.
An integer that is equal in magnitude to the sum of their absolute values. Its sign is the same as which of the two numbers you are taking the difference from. For example, for the integers 5 and -7. Their absolute values are 5 and 7 so that the sum of the absolute values is 5+7 = 12. Then 5 - (-7) = +12 and -7 - 5 = -12.
opposites, additive inverses
The set of whole numbers includes all their additive opposites. So the set is the same as the one you started with.
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.