There are very good reasons to accept inifinite types of constructions. All of calculus is basically inifinite limits. Thats from what I've read, to the uncomfortable but necessary acceptance of formal infinity. A simple example I like is Zeno's paradox. You take one step of size 1 on first second, half step in next half second etc. This is just breaking apart the act of two full steps done in two seconds, yet we can describe it as an infinite sequence of smaller and smaller steps (1, 1/2, 1/4 adds to 2).