There is not much to prove there; opposite numbers, by which I take you mean "additive inverse", are defined so that their sum equals zero.
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
"Size zero models" are used to describe female models that are able to fit into a size zero clothing (dress, pants, shirts,etc.).
Two numbers that are the same distance from zero on a number line are called "opposites." For example, +5 and -5 are opposites, as they are equidistant from zero but lie on opposite sides of it. They have the same absolute value but different signs.