Zero
A zero pair
The answer depends on what is meant by "their opposites". If you mean additive opposites then the set is of all non-zero integers.
It is zero and that is simply because that is how additive opposites are defined.
Zero
Their total is zero.
Because by definition, there sum will always be zero. Because the definition of opposites are additive inverses.
opposites
These are the integers.
additive inverse property
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adding one to minus one = zero.