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I am writing a theorem, and in it, I mix $\frac ab$ and $a/b $. The reason for this is that I find

$$\lceil a/b \rceil \tag{1}$$ better-looking than:

$\displaystyle \biggr \lceil \frac ab \biggr \rceil \tag{2}$

or

$\displaystyle \lceil \frac ab \rceil \tag{3}$

or

$$\textstyle \lceil \frac ab \rceil \tag{4}$$

$(2)$ looks weirdly proportioned, and in $(3)$, the ceiling function is too small for the fraction. In $(4)$, the fraction is well-proportioned, but a bit small, making it harder to read. In addition, when used with $\displaystyle \frac ab$, it will lead to differing sizes of the terms, which lookes a bit weird to me. Example: $\displaystyle \frac ab - \textstyle \lceil \frac ab \rceil$.

However, I find $\frac ab$ better-looking than $a/b$, and also easier to read, as I'm not too used to using and reading the slash as a divider. This leads me to mix the two types of dividers. Whenever there's a ceiling/floor function involved, I use the slash, and when there's not, I use the fraction. So my question is, is this common and accepted? Using the $\div$ is apparently not common and "accepted", and since there seems to be a consensus on that, I suspect there may be a consensus on mixing types of notation. If there isn't a consensus, then this question does not have an objective answer other than "there is no consensus" or "there is no consensus, but the majority of papers (...)". If that's the case, I'll accept the answer.

EDIT: The context is me writing an applied math paper (applied to the field of organic chemistry). It involves combinatorics and number theory.

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    $\begingroup$ This is a perfectly valid and motivated question and I am sorry to see that it is being downvoted. $\endgroup$ Oct 6, 2021 at 17:43
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    $\begingroup$ No I don't, but seeing that you raised that question on Meta, I hope you get an explanation there. $\endgroup$ Oct 6, 2021 at 18:02
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    $\begingroup$ I guess that the downvotes and close votes were because it's more about typography than actual math. But I don't know of any better place for questions about mathematical typography. $\endgroup$
    – md2perpe
    Oct 6, 2021 at 18:56
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    $\begingroup$ @md2perpe You commented about mathematical typography. While I hate to assume that the existence of a tag implies that questions in that tag are on topic, TeX.se does have a typography tag which appears to be active. From the tag wiki there "Questions tagged typography deal with ... and, incidentally, questions about what constitutes good typography in the first place." $\endgroup$
    – Xander Henderson
    Oct 6, 2021 at 20:41
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    $\begingroup$ I think this is fine as a question under the article-writing tag. I don't think there is any agreed convention about $a / b$ versus $\frac{a}{b}$, but I would not use $a \div b$ without some very good reason. A convention that I often follow and seems to work well with many of the styles that journals impose is to use $a/b$ in formulas in running texts and $$\frac{a}{b}$$ in displayed formulas. You should certainly use \left\lceil and \right\rceil to get the right size of ceiling symbols $$\left\lceil \frac{a}{b}\right\rceil \quad\mbox{not}\quad \lceil\frac{a}{b}\rceil$$. $\endgroup$
    – Rob Arthan
    Oct 6, 2021 at 21:21

1 Answer 1

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Per Section 13.10 of the AMS Style Guide:

Fractions in text may be case (stacked) or slashed.

and

Fractions need not be consistent (either case or slashed) throughout a paper, just within a math phrase.

So while I'm not sure there's any convention specifically for fractions within a floor/ceiling, generally speaking you're free to typeset fractions either way, to maximize legibility and tidiness of the expression, on a case-by-case basis.

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