Yep. ∞ is infinitely big in the same way that 0 is infinitely small. -0 = 0 and -∞ = ∞. Opposite ends of the circle. (Or the Riemann sphere if you like complex numbers.)
While this Riemann sphere seems like a useful concept, -∞ = ∞ is an observation that doesn't seem to hold true outside this spherical model of complex numbers. Just add ∞ to the both sides, and you end up with 0 = ∞ + ∞ which is most certainly not true.
adding ∞ to both sides does not create a ∞ - ∞ situation, though. The substraction is a whole different topic, because it becomes an elimination problem, whereas ∞ + ∞ = ∞
Sure. And it also doesn't help to avoid the problems with division by zero. But lucky we're posting in the shitpost section, so we don't have to worry too much about details.