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A Mathematics lecturer can’t find a nice exercise for the final exam paper of his course. Then he makes up his mind and gives the following one-line exercise:

Write an exercise you think suitable for this exam, and solve it.

When he corrects the papers, he finds out that - just under the text of this exercise - one of his students has worked out the following two lines:

Write an exercise you think suitable for this exam, and solve it. Write an exercise you think suitable for this exam, and solve it.

Now, the question is: Is this a correct answer to the exercise? If it’s not, modify it so that it becomes a correct answer.

I think it should be modified, because to solve the first sentence i need to solve the second and then i should solve the third, but to solve the third i need to write another exercise and solve it, so he should write infinite lines. But i don't think this could be the correct answer. So i don't know how to solve it, also there is more than one answer

Lex
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    Is that logic? It sounds more like natural language and [its] semantics. – Asaf Karagila Jan 16 '14 at 17:12
  • @AsafKaragila english.stackexchange? – Tim Seguine Jan 16 '14 at 17:19
  • @AsafKaragila I would say that "how can we troll this question in a mathematical way" is a valid question for this site with respect to topic (of course, there might be other flaws, like being opinion-based and so on). I think the OP asks about mathematical way to tie the loose ends (e.g. avoiding the infinite sequence of sentences), not about semantics of a particular wording of the cited phrase. – dtldarek Jan 16 '14 at 17:44

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My solution would be:

Excercise: Write an exercise you think suitable for this exam, and solve it. Solution: see Excercise and its Solution.

Then it is recursive in its definition. It relies on self reference and the lecturer considering the question as posed a suitable question. Logically this must be, since they posed it. And lecturers don't pose unsuitable questions (if economists can assume rational behavior, so can I).

Tim Seguine
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  • So you obtain a sort of circularity. Is it a paradox ? Has it something to do with the discussion about the possibility of building paradoxes (like the Liar) avoiding self-reference ? (see http://en.wikipedia.org/wiki/Yablo's_paradox) – Mauro ALLEGRANZA Jan 16 '14 at 17:23
  • Almost perfect, the problem is that your "Solution" is not a part of "Exercise" and so "see Exercise" is not a full solution (it lacks a solution you requested). I would say that "Solution: see Exercise and its Solution." would be better. – dtldarek Jan 16 '14 at 17:32
  • @dtldarek agreed. I have modified my answer. – Tim Seguine Jan 16 '14 at 17:42
  • @MauroALLEGRANZA not a paradox. It is just self-referential. – Tim Seguine Jan 16 '14 at 17:50