A distinction can be made when considering the limit of a sequence. If a sequence converges to zero from positive values (sometimes written -> 0+), then the inverse of the sequence will diverge to +inf, while if the sequence converges to zero from negative values (-> 0-), the inverse will diverge to -inf.

As a sibling comment wrote, rounding numbers to -0 and +0 can provide extra information, though it may not be useful in all contexts.