The man in this paradox will never catch up to the tortoise, let alone overtake it, because as the man gets to the tortoise's initial position, the tortoise would have moved forward more. He will never actually catch up to the tortoise because of this. This is similar to Zeno's paradox because in this paradox, the man will never actually reach the wall because he keeps on taking steps that are half the size each time. There will always be a gap between him and the well. After an infinite amount of time however, the man will catch up to the tortoise and overtake it and the other man will eventually reach the wall in real life. This is because the ratio is 1/2 and it is convergent.
Moreover, I agree with the answer of .5 because .5 is between 0 and 1. It is impossible to know what the correct answer is. Also, this relates with what we have been studying as it relates to the alternating series. I believe that the reasoning behind Thomson's lamp dilemma makes sense because there can be multiple answers.
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