Yeah. Great mind teaser. I can imagine an imaginary number (-/+) "inf" for divisions by number approaching zero from left/right, yet the algebra would not be possible to define properly because you can approach zero with a different rate.

The undefined cases, where the left/right limits are not equal coulf get imaginary number "shrug" because it would be even less useful.

Of is anyone able to define a useful algebra for these? I'm really curious.