<p>I think that <em>to acknowledge or not to acknowledge</em> depends on how much help you get in the answers. See for example <a href="https://stats.stackexchange.com/q/31679/10525">this question</a>. </p>

<ul>
<li><p>If you just clarified some ideas or concepts with the question, then I think it is fine not to acknowledge SE-users. Answering this sort of questions is one of the goals of SE sites and we all know that what we post here becomes of the public domain.</p></li>
<li><p>On the other hand, if the question triggered or improved an idea that became a paper through a substantial involvement of one or more of the responders, then acknowledging this person(s) may be more ethically correct. Some SE users go beyond the question and provide proofs of new results or code. If you are planning to use them or include them in a research paper, then acknowledging their contribution is more correct, I think. If this is the case, you can let the user know through a message in the corresponding answer and see his/her opinion. It might be the case that the responder do not want to be acknowledged.</p></li>
</ul>

<p>In addition, typically you just have to acknowledge for "helpful discussions" without providing further details unless there is a special reason for doing so (such as including a result proved by the other person, a code, helpful/crucial references, or an original idea).</p>

<p>In my opinion, <a href="https://stats.stackexchange.com/q/45842/10525">your question</a> asks for clarification of a well-known result. I do not think it is necessary to acknowledge the responders unless you want to use the counterexample provided by @whuber. The rest of the contributions seem to be general pointers to me.</p>

<p>I have found some related discussions in <a href="https://academia.stackexchange.com/questions">Academia-SE</a>:</p>

<ol>
<li><a href="https://academia.stackexchange.com/q/1580/3836">Attributing contributions to academic work that occur in Stack Exchange</a></li>
<li><a href="https://academia.stackexchange.com/q/4891/3836">Academic discretion: Should one participate in online forums or Stack Exchange sites anonymously?</a></li>
</ol>
