What is the additive inverse of infinity

Dear student
In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation.
Infinity isn't a number and thus we cannot apply arithmetic operations to it.
Thus $\infty -\infty \mathrm{does} \mathrm{not} \mathrm{make} \mathrm{sense}.$