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I got into a debate with a friend about a month back and this question has been racing through my head ever since. Does Math necessarily reflect what's real?

He asserted that Math can give you results far-off from what's real. He illustrated his claim like this: Suppose you want to build an average-sized building. You employ some workers for the job and and then estimate mathematically the time the building should take to complete. You get a certain estimate but it occurs to you that if you employ more workers, it should take less time. Suppose then that if you add just enough workers, your calculation would give you a time estimate to complete the building of 5 minutes. But that is impossible in reality. No matter how many workers you add, you can not build and average-sized structure that fast!

There has to be something gravely wrong in his reasoning but I can't pinpoint it. I'm not good at anything and I actually feel embarrassed bringing this stupid argument up here to you people of such high understanding; but science and math are the only two things in the world I have my full confidence in and the idea that math can be so disjointed from reality is making me very uneasy.

I tried to keep it as short as possible to ensure that I do not consume too much of your precious time, but I guess I failed. I'm sorry about that.

So, what's your take on this?

Thank you so much for your time! ^_^