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In CSE, we can use TeX. This makes it possible to do a number of things in comments, like (approximately by increasing questionableness)

  1. using “$k=\log_2(N)$” to insert a simple formula
  2. using “$\;$” to insert a wide space
  3. using “$$k=\sum_{j=0}^{j^2<n}2^j\cdot\log j$$” to insert a formula alone on a line, or/and more readably formatted
  4. same as 3 for multi-line formulas
  5. using “$$\text{ventricules in the framistan}$$” or “$$\mathtt{foo=bar+zoo}$$” to emphasize a citation in what's being commented
  6. using “$$$$” to insert the equivalent of about 2 entirely blank lines

This comment shows 2 and 5 at work.

Where's the line between acceptable and abusive?

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From my point of view, the comment you’ve linked to makes sense as-is. So, I personally would say it’s fine in that particular case

But: sometimes (hinting at your linked case… but then again, the question is off-topic in itself) starting to write TeX in a comment may just point at the fact that that comment could be a worthy answer… which means that before hitting the “post comment” button, everyone should do a self-check to see if he/she isn’t actually posting an answer as a comment (which I think would be a shame, because in that case it most probably deserves upvotes and maybe even an “accept”… which isn’t possible to do when the answer was posted as a comment).

Aside from that, the only thing that actually has a chance to worry me is the $$$$ case which inserts two (or more) entirely blank lines. To be honest, I wasn’t aware of that one yet. The problem I see with that one is, that it would add too much whitespace, pushing the page into unnecessary length (thereby destroying a bit of the usual, overall readability). I think that would somewhat mark the line of “pushing it to the limits”.

So, the line between acceptable and abusive would be somewhere between using a bit of TeX to make a comment clearer (like what you’re linked to), and using multiple instances of $$$$. After all, a simple comment with a bit of $$LaTeX$$ still looks fine and may even enhance readability of that comment. But it would start to look a bit abusive when using something like $$$$ $$$$ $$LaTeX$$ $$$$ $$$$.

Providing some visual examples:

  1. Acceptable: TeX centered on it’s own line looks fine.
    (Especially when sharing somewhat long formulas.)

    TeX centered on it’s own line.

  2. Acceptable: TeX within the text looks good too.
    (Depending on what’s TeXed, is might even look better/cleaner.)

    TeX within the text.

  3. Abusive: Multiple blank lines don’t really make sense in a comment.
    (And there are less obnoxious ways to grab attention.)

    Multiple blank lines wrapping the actually important stuff.

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    $\begingroup$ What about peppering comments with LaTeX whitespace in an effort to pretty-print them, even though it doesn't really work reliably on all browsers and configurations (and slows down the rendering by a minute amount)? $\endgroup$ Commented Jul 23, 2014 at 13:08
  • $\begingroup$ @Thomas As I noted above… if you’re doing that, chances are you’re actually posting an answer as a comment. In the end, we have to remember that comments once started out as a way to ask for clarification, not a means to post non-down-voteable answers. ;) /* Re: “non-down-voteable“ …did I just invent that word? Hope it makes sense nevertheless. */ $\endgroup$ Commented Jul 23, 2014 at 15:14
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I think you should only use it for formatting math. I.e. 1. and maybe 3.

Newlines in comments in general haven't been added despite requests. As I haven't seen a good reason for declining, it seems like the least abusive abuse.

For emphasis there is already *italics* and **bold**, which are semantically correct since they use <em> and <strong>.

Regarding the linked comment, I would have preferred `backticks`, since that's again semantically correct for code.

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