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1) A man wants me to go from a to b in a straight line.
2) Suppose he can, first he needs to go to (a-b)/2.
3) Suppose he can, secondly he needs to go to (a-b)/4.
4) There are infinitely many integers.
5) He can never arrive at b.

Anyone can help me break down this trap? What is this idea known as?

  • 4
    This is called Zeno's Dichotomy Paradox. – Nick Mar 31 at 18:14
  • thank you!Was looking for the name – Chenang Zhang Mar 31 at 20:58
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The answer in analysis is to identify the result of all the “infinitely many integer divisions” with the end point.

Yes, you’re right, at any finite subdivision along the way from point a, you haven’t yet reached point b. However, once you say you’ve genuinely stepped through the infinitely many sub distances, then you have found yourself at point b. This is what we mean when we talk about the limit of a converging series with a variable tending towards infinity being well defined.

This is possible in reality, as Aristotle understood, because Time is also a relevant dimension in motion and you pass each of your gradually shrinking distances in gradually less time. The time dimension can also be factored into analysis and it’s limits defined and understood in the same way.

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