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I was happy to find out that my intuition about setting differential operators and common math constants was right (see the accepted answer).

However, this got me thinking. My rationale for using upright 'e' and 'i' for Euler's constant and the imaginary number was that these are the names of some specific numbers. So just as one sets sin upright because it is the name of the trig function, one sets the constants upright...

But what about the function $f(x) = x^2$? It seems to me that this gives a name to the function $x^2$, so by the reasoning above one should set f upright... I do not like this, and nobody does it that way.

What is the difference between the two situations?

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yrodro
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    As I understand it, the upright convention for 'e' and 'i' stems from their being constants, not variables. Variables (scalars, at least) are traditionally typeset in italics. Since functions are comprised of any number of variables, they "inherit" the variability. (Disclaimer: I'm just an engineer, and mathematicians probably have many horrible things to say about my logic here.) – Paul Gessler Oct 30 '14 at 04:43
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    But anyway, while these questions are always interesting to us, questions about these sorts of conventions are not really on-topic for this site. The ones that sneak by do so because they have an added component of "and what's the recommended way to follow said convention in LaTeX?" – Paul Gessler Oct 30 '14 at 04:45
  • Excuse me for asking but what do you mean by upright? – Adam Oct 30 '14 at 04:51
  • @Adam: In $e \mathrm{e}$, the only the second e is upright. – Peter Grill Oct 30 '14 at 04:56
  • This post may solve some of your concerns http://tex.stackexchange.com/questions/34905/when-should-math-be-upright – Adam Oct 30 '14 at 05:00
  • I wouldn't be surprised if some country's typographic traditions at some point in time mandated the use of upright letters for function names. When Knuth set out to create TeX, he did a very careful study of the principles that guided the math typography of several leading math journals over a span of several decades. He discovered a huge amount of variation -- much of which seemed to be due to general sloppiness as well as an absence of consistent design principles... His choices, in the end, are as much an act of human creativity as an implementation of well-codified standards. – Mico Oct 30 '14 at 05:37
  • Whilst this is an interesting question, it's very much tangential to the scope of the site. At a technical level it is easy to create upright letters in math mode (contrast say \pi, where more technical effort is required). – Joseph Wright Oct 30 '14 at 07:25
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    Unlike technical drawings and engineering conventions, math notation is for conveying specific ideas about logical chain of argments. The linked question only mentions a standard and also much of the comments question the validity of any standard. So there is no rule and also this is unfortunately not a TeX problem but a personal taste. It doesn't matter if f is upright or not as long as the readers understand what you mean by f(x). – percusse Oct 30 '14 at 08:28
  • f is a locally defined variable just like x, just members of different sets (or types depending on your foundational view of mathematics) either way I'd expect them to be in the same font. – David Carlisle Oct 30 '14 at 10:12
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    I do not agree with those who say this is off-topic. I've never, ever, questioned if a function has to have its name in italics or upright outside the TeX world. If this question is on topic somewhere, it's definetly here. – Manuel Oct 30 '14 at 11:09
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    I voted for off-topic. It's a matter of style and has nothing to do with TeX. The fact that I hate seeing “e” and “i” upright is only tangential. In any case, “f” is just a common name, not a specific one, like for “sin” that always denotes the same function. – egreg Oct 30 '14 at 11:28

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The document you quoted in the post linked above explains it:

According to the ISO regulations and the IPU recommendations, italic symbols should be used only to denote those mathematical and physical entitiesthat may assume dierent values [...]

This way the reader can distinguish between any e used as a variable, and Euler's number. I like to think of it like of the difference between a regular and a proper noun. The function f is x |--> x^2 in your document and maybe x |--> 2*x in another one. The imaginary unit i however is always the same thing. (Likewise, the word "book" in one text means an entirely different book as in another text. When mentioning "Austria" however, completely unrelated texts refer to the same country.)

黄雨伞
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  • According to Wikipedia: "Austria was, according to the early medieval geographical classification, the eastern portion of Langobardia Major, the north-central part of the Lombard Kingdom, extended from the Adda to Friuli and opposite to Neustria." So Austria is not only used to denote one and the same thing. Just like i does not always denote imaginary unit. And even that imaginary unit is only unique up to a sign. – Michael Jan 17 '18 at 12:24
  • @Michael nice fun fact, but my point remains – 黄雨伞 Jan 18 '18 at 13:38
  • My point is that it's an illusion to believe that there is a global scope of names upon which everyone agrees. Taking the ISO regulation at face value: if I decided to call the function x|-->x^2 by the name f in my document, than in that document it is a proper noun (a constant) and f should be set upright. Irrespective of what people do in other documents. – Michael Jan 18 '18 at 14:43