What is acceptable when answering or commenting on problems you don't necessarily know the answer to?

I have been learning a lot of mathematics over the past few years from reading problems and solutions on Math.stackexchange and then using the techniques I gained from them to eventually try answering other questions.

However, I felt that in the last while I never answer a questions anymore because it seems like the difficulty of problems being asked here are much more difficult than when I started. Recently, if I don't repeatedly refresh the page looking for a more elementary problem, I can only contribute if I answer questions that I feel are a little outside my abilities.

Where is the line drawn when posting something you are not 100% confident in?

Here is one example.

At the time I saw it, this post was about 30 minutes old with no comments or answers for what I thought was simple enough to get a near instant response but something just outside of my ability to answer. (This isn't a very large amount of time, but I've encountered similar situations in the past with 24+ hours on the question's age)

I had written up the following comment:

I am casually teaching myself functional analysis so take this comment with a grain of salt, but I believe that since $f$ is linear and bounded, $f$ is continuous, and you need this to write $f(\lim_{n\rightarrow\infty}\sum_{i=1}^{n}\alpha_{i}e_{i}) = \lim_{n\rightarrow \infty}f(\sum_{i=1}^{n}\alpha_{i}e_{i}).$

I wasn't too confident because in my attempts to learn about various spaces you see in functional analysis, often times a small change in a topological properties makes many fundamental properties no longer true.

I felt that in this situation, even if I preface my comment with a warning, the site is better off if I didn't comment at all.

Something like this probably happens at least twice a week for me. Due to its frequency, I am curious what more experienced users thoughts are on this matter.

• I think this is ok. It may be better to post such material as a comment rather than as an answer. They often also serve a dual purpose as a request for clarification. I would be hesitant to post something I'm not sure of as an answer unless may be a day has passed (without a detailed full answer). Sometimes the question is tough enough so that a report of partial progress, or a description of an idea (that is too long to fit into a comment) may be a useful contribution. When doing that my goal is to "get the ball rolling" rather than to settle the question once and for all. – Jyrki Lahtonen Jun 7 '16 at 8:04
• This seems related - although only to some extent: Should I be hesitant to answer questions? and Letting less-reputable people answer questions. – Martin Sleziak Jun 7 '16 at 13:56
• BTW the way you phrased your comment seems reasonable to me. And in the meantime somebody posted a comment exactly about argument based on continuity. – Martin Sleziak Jun 7 '16 at 13:58
• Comments like that can be quite useful, and your wording is fine. You should definitely consider posting at least some of the comments of that kind that occur to you. Not only are they potentially helpful to others, but you may well get useful feedback either confirming what you thought or indicating where you went astray. – Brian M. Scott Jun 13 '16 at 23:09
• One more comment. If you are hesitant to answer or comment on the actual post, you can still ask in chat something along the lines: "I was thinking about this question. Is the following argument correct?" In this specific case you could ask in the main chatroom or in the functional analysis room. (Although the latter is rather inactive lately.) Maybe you will receive no response, but there is at least some chance that you will get some feedback. – Martin Sleziak Jun 15 '16 at 6:39
• I have the same problem every so often, and for me, I usually would post such information as a comment. One way around this, as I have noticed, is to slack off from the site for a few days and come back. Another way is to visit other tags you feel comfortable with so you can have a more varied plate. – Simply Beautiful Art Jun 15 '16 at 11:28