Infinity is one of the most useful tools in physics, which is the study of... reality. One example that's rather easy to visualise is the repelling force of opposite charges; how large would you expect that force to be if they are right on top of each other? Besides values that can obviously be (-)infinity, there's also theories about infinitesimally small particles and an infinitely large universe. Infinity is not a mathematical construct, and I'm not entirely sure how you could claim that infinity has no basis in reality.
Oh, right. I'm used to other solutions being redundant or useless, to be honest
Only when coming from the positives. And I've heard it's even worse on the complex plane, but I've not looked at that myself.
Oh, right. I'm used to other solutions being redundant or useless, to be honest