It's not positive or negative infinity. It is simply undefined. Math has many conventions, and you can define your own convention that it does equal some flavor of infinity, but that is only a convention, and not a universal one.

That's not the problem, and this is not just pedantry. It's just not correct to say that n/0 = inf, nor even to say that positive_n / 0 = inf, in any normal math context.

For example, if you accepted that n/0 = inf just like n/1 = n, then you'd conclude that n/0 + 3 = inf + 3 = inf, so n/0 + 3 = n/0, so 3 = 0. Or you'd want to do weird things like asking what is sin(inf).

All discussions of mathematics assume maximal possible pedantry.