The question cannot be answered sensibly for two main reasons.
First, the question mentions "there opposites" but does not specify WHERE the "there" refers to. Second, opposites are defined in the context of some operation. The opposite of 3 with respect to addition is -3 while the opposite with respect to multiplication is 1/3. There are other operations which will give yet more "opposites". There is no way of determining which one you mean.
The set of whole number and their opposites is simply the set of whole numbers!
The opposites of whole numbers are also whole numbers: both sets are the set of integers.
The set of integers (ℤ) is the set of the positive whole numbers and their additive opposites (the negative whole numbers).
Apart from zero (which is its own opposite), the opposites of whole numbers are also whole numbers. You have the set of whole numbers which is also known as the set of integers.
integer
Integer
INTEGERS
The set of whole numbers includes all their additive opposites. So the set is the same as the one you started with.
integers
J
That is called the set of "integers".
Apart from zero (which is its own opposite), the opposites of whole numbers are also whole numbers. You have the set of whole numbers which is also known as the set of integers.