Positive integers, if I understood you correctly
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Two integerss add to zero when their absolute values are equal and they have opposite signs.
That will depend on the two integers that you use. The result could be any of negative, zero or positive.
diffrence will always be positive except when it is zero but is you speak of substraction operation it can be positive negative or zero
They will comprise the set of non-zero integers.
Their quotient is positive if the integers have the same sign;negative if the integers have different signs;zero if the dividend is zero (and the divisor is not).