As a counter-argument: why are we generally ok with allowing things to be infinite when they're expected to be finite? Precise bounds are obviously best, but s

As a counter-argument: why are we generally ok with allowing things to be infinite when they're expected to be finite? Precise bounds are obviously best, but sometimes it's not efficiently calculable or not worth the effort - don't choose the literal worst possible value there (infinity), pick something that'll stop itself when it goes insane. And no, it's a tool. Use it where it makes sense.