Should I post an answer to my question which doesn't answer the specific question, but is relevant and helpful?

Question

Several months ago, I asked a question about whether or not a certain operation was used in mathematics. I then went on to explain this operation in some amount of detail. I recently decided to come up with a (surprisingly simple and elegant) proof that my operation does what I claim it does, and I would like to add it to my question in some way.

The proof, however, doesn't add anything to the question, but it's not an answer to my question, either. That being said, I feel as though the proof would add to the discussion.

What should I do in this situation? Would it be frowned upon if I edited my question in a way that made my proof on-topic?

Answer 1

Option 1: Post an Answer

It is common and generally accepted to post tangential thoughts as answers to questions. This often makes sense when the OP or other people who searched for the OP's question might find whatever you have to say interesting. Your situation seems to fit this scenario.

So, just post an answer with your proof. Say at the top of the answer something like, "readers of this question maybe interested to know the following tangential result..." or, "this is not an answer to the question, but..." to alert readers right away that you aren't answering the original question.

An example of such an answer is here. Everyone appreciated the input though it was not an answer to the original question.

Option 2: Edit the proof into your question

It is also common to simply edit your question. At the end, say: "EDIT: This is a bit tangential, but I found a proof of ____, here it is:"

A warning

Whichever of these two options you choose, do not edit your original question to change what you are asking. This will throw off people who have already looked at or answered your question. Your new proof is not an answer to the original question and you shouldn't change the original question just to make it more appropriate.

Answer 2

I would suggest that you pose a new question and link to the old question as a reference. Additionally, you might add a link in the old question to the new as a relevant follow-up question.