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Yesterday I wrote an answer to Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?, but it was deleted despite being correct as far as I can understand:

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I didn't feel the need to explain the $x$, because the asker had already used it the same way and I stated his $x = 1 - 1/x$ equation was right, but I just fail to see how my answer "does not really answer the question". Is this site against short and simple answers (example: http://meta.math.stackexchange.com/questions/16925/why-was-my-answer-deleted-by-a-moderator), or is there something factually wrong with my answer? Or should I just have explained the $x$ further?

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    $\begingroup$ I can only speculate what the delete voters thought, but I guess they were concerned about the fact that the first problem with this continued fraction is convergence. Or, even before that, whether even the truncated fractions exist, and form a sequence. IMHO those problems, rather than any attempt to evaluate the limit, are the key to this question. $\endgroup$ – Jyrki Lahtonen Mar 8 '16 at 12:59
  • $\begingroup$ Mind you, some other answers to that question suffer from the same problem (lack of attention to convergence), so it looks like there may also be something else. $\endgroup$ – Jyrki Lahtonen Mar 8 '16 at 13:05
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    $\begingroup$ It seems that the OP knows that $x=1-\frac1x$ has no real solution. They show that the only solutions are complex numbers. Your proof showing the same thing might be useful as a comment showing another way to show this, but it definitely does not provide an answer to the question. $\endgroup$ – robjohn Mar 8 '16 at 13:28

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