If I start at 1 and my goal is to get to 2, I could move to 1.1 and be a little bit closer to 2. Then move to 1.11, and be even closer. Then 1.111, so on and so forth. I understand that with each move, the step forward is smaller than the previous one. But it’s moving forward nonetheless. How is it that I can forever move forward, but never get there?
In: Mathematics
Because each step is smaller. your first step is 0.1, then 0.01, then 0.001 and so on, eventually the step is infinitely small. This is a good example of the key difference between pure math and something like engineering or physics. Theoretically, you never approach 2. In reality, the steps will get so small that you can’t actually measure them. You won’t be able to accurately take the step, or determine if you’ve actually stepped. You’ll get to the point where you don’t know if you’re at 1.111, 1.113, or 1.105.
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