Consider that lim -> inf does not mean “It goes to infinity”. Its actual definition has nothing to do with infinity. So your argument about infinity is a red he

Consider that lim -> inf does not mean “It goes to infinity”. Its actual definition has nothing to do with infinity. So your argument about infinity is a red herring. Or try it the other way, tell me what mathematics works better if 1/x=0 than 1/x=5. If there’s an aesthetic preference displayed here, it’s for mathematics as a tool for reasoning.