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
Another way to think about it is, in order to reach 2 from some lower number x, you eventually have to take a step that’s at least as large as the distance from x to 2, which is 2-x. With the procedure you described it’s like you’re actively avoiding taking a large enough step: if you’re at x = 1.1, you’re 0.9 away, but taking a step that’s too small to even get to 1.2, which is only 0.1 away. And so on; the next step is lower than 1.12, then the next one is like you’re trying to stay lower than 1.112, etc.
You’ll never reach a destination if you’re always taking steps that are chosen specifically to be smaller than the remaining distance.
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