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Question: Find all connected and path-connected subsets of $\mathbb{Q}$

We've shown that the connected subsets of $\mathbb{Q}$ are all sets that contain exactly one element of $\mathbb{Q}$.

Now our reasoning is as follows: Since path-connected subsets of $\mathbb{Q}$ are connected as well, all path-connected subsets of $\mathbb{Q}$ are only the single-element subsets as well.

Is this reasoning correct?

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Yes, it is correct. – Antonio Vargas Jun 1 '12 at 15:42
That was quick. Thanks :) – gnirx Jun 1 '12 at 15:44
up vote 4 down vote accepted

Yes.$ $

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