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This is related to this question: On the inclusion of pages-of-text-as-images in questions and inspired by this answer of mine: https://math.stackexchange.com/a/100984/2614

So, the discussion in the other meta question specifically addresses the inclusion of images in questions. What about answers?

In the answer I linked to, my motivation for posting a full proof out of a textbook is the following. I believe the question posed by the OP is very natural and deserves a clear exposition; however, I remember the proof of the fact being quite involved. I remembered reading it in Warner, so instead of just linking to Google Books, I thought it would be nice to have a complete, readable answer to a good question in math.SE. But it somehow makes me uncomfortable, answering a question like that (not that I would do it frequently).

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    $\begingroup$ Are you worried that the images might get removed without notice, leaving your answer incomprehensible? Or are you uncomfortable because you didn't take the pains to type it out? (FWIW: I believe that the latter is not really an issue.) $\endgroup$ – Srivatsan Jan 21 '12 at 15:40
  • $\begingroup$ @Srivatsan: A part of the reason for asking the question is that I did feel a bit uncomfortable earning reputation for a solution out of a textbook. Indeed, I thought of the reference myself, and indeed, I made the effort to post the images, but it feels a bit like cheating. Perhaps such answers should be community wiki? (I'm not suggesting it, I'm merely thinking out loud...) $\endgroup$ – Bruno Stonek Jan 21 '12 at 15:44
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    $\begingroup$ Are there any legal (copyright) issues in posting an excerpt from a textbook? $\endgroup$ – Srivatsan Jan 21 '12 at 16:14
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    $\begingroup$ @Srivatsan It is quite common to see almost exactly the same proofs of theorems published in many textbooks. So to worry about copyright issues due to analogous duplicity here is a bit absurd. There are much better things we could do with our time. $\endgroup$ – Bill Dubuque Jan 22 '12 at 0:01
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Answers are meant to be enlightening and useful, but not necessarily original. As long as the sources are properly attributed, I do not find any issues in posting an excerpt from a textbook as an answer.

In fact, it's very likely that the exposition in the textbook is hard -if not impossible- to improve upon. So there may not be any point in rewriting the content or style just for the sake of putting in additional effort.

To give an example from my own posts, in one of my answers about uniformly continuous functions, I quote an approach verbatim from Erdman's ProblemText. I like the presentation of the theorem and did not want to modify it (even though I believe I could have). The only difference in that case is that I typed out the relevant paragraphs rather than post an image, because I was worried about the persistence of images in this site; but this does not seem to be the OP's concern in this post.

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I deleted the image not because it was an image but because I am concerned about the copyright implications. I would be much more comfortable if you obtained permission from the copyright holder before posting it.

StackExchange doesn't currently have an official policy about such issues, but what with recent events I think it would be prudent to be cautious.

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    $\begingroup$ I understand your concern. As a note, I took the screenshots directly from Google Books, which made the previews freely available (alas, in the weird world of copyright, I wouldn't be surprised if posting the same freely available content on a different site were not legal). $\endgroup$ – Bruno Stonek Jan 21 '12 at 22:18
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    $\begingroup$ I have reverted the deletion. Such action should only be taken if the majority of the community agrees it is correct - not a lone member. $\endgroup$ – Bill Dubuque Jan 21 '12 at 23:54
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    $\begingroup$ @Bill: fine. If the community wants to open itself up needlessly to the possibility of legal action, that's the community's decision. $\endgroup$ – Qiaochu Yuan Jan 22 '12 at 0:10
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    $\begingroup$ @Qiaochu I've been using the net heavily for a few decades. I've never once seen a problem arise due to such fair-use excerpts of mathematics publications. They are free advertising, so publishers would be foolish to discourage such. $\endgroup$ – Bill Dubuque Jan 22 '12 at 0:16
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    $\begingroup$ At present we shouldn't have to police for copyright infringement, nor pre-emptively restrain ourselves for that purpose, because legal action for such against a user-driven content site should not be taken without first giving MSE and mods fair warning for takedown, if I understand things correctly. PIPA/SOPA are not currently law and may not be put into law in their current forms, so I don't feel we're opening up ourselves very wide at the moment. At any rate, I'd rather risk it (to the degree risk exists) for the sake of openness here, and the community might largely feel the same way. $\endgroup$ – anon Jan 22 '12 at 3:11
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    $\begingroup$ @bruno: There would be nothing weird about the situation if Google has free previews that were infringement elsewhere. The copyright holder has the right to license Google to distribute the content without extending that same license to everyone (or anyone) else. An analogous situation: my contract with my publisher allows me to distribute my book from my web site, but that permission does not extend to other people distributing it from their web sites. $\endgroup$ – MJD Jul 19 '12 at 18:38
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In this particular instance, the number of pages posted is more than I personally would be comfortable with posting, though I couldn't give you a clear rule on how many pages would be okay. My not-a-lawyer understanding of U.S. Copyright Fair Use is that, horrifically unfortunately, the only way to determine whether a use of a portion of a copyrighted work falls under fair use is to litigate over it, so I don't think there is a clear rule in U.S. law, either. My general feeling is: a page or two of a book, with a proper citation and note of copyright, is probably fine; posting a copy of a whole book without permission (or a link to such a copy of the whole book) is not (and this has actually come up here before); your use is somewhere between these, and probably closer to the okay side than the not-okay side.

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