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September 14th, 2014, 12:41 AM   #1
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Italic text in mathematics

It sounds like there is ISO standard (physics.nist.gov/cuu/pdf/sp811.pdf) to let variables be typeset in italics in mathematics. For example, the variable x is always typeset in italics:
\[
x= 3
\]
What about sets? It seems Wikipedia has made it its standard to typeset sets in italics. There is even an article (Wikipedia:Manual of Style/Mathematics - Wikipedia, the free encyclopedia) instructing people to typeset sets in italics. We let A be a set, then we refer to A in this way, using italics: \[
A = \{x\,|\,x > 3\}
\]
However, Wikipedia and many other documents I have seen do not typeset the hollow type fonts used to denote the real, complex numbers etc in italics. Which makes me wonder; why not? This must be a contradiction. Is this because the standard fonts which come with most latex distributions does not have this feature, or is this some sort of official standard? Shouldn't the sets we let denote the real numbers, complex numbers etc $\mathbb{R}, \mathbb{C}$ be typeset in italics too? After all -- they are just sets, like $A$.

What is the convention, and why?

Thank you for your time.

Kind regards,
Marius

Last edited by king.oslo; September 14th, 2014 at 12:53 AM.
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September 14th, 2014, 07:27 AM   #2
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My guess is the reason ordinary math symbols are in italic is to set them apart from the surrounding text. If you used an upright A to call a set and started a sentence with it (which is not recommended even with the current convention), you would get, e.g., "A is the union of...", which looks confusing. On the other hand, $\Bbb A$ is not going to be taken for an article even if it upright.
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September 14th, 2014, 08:10 AM   #3
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There are lots of rules for the typesetting of mathematics. Many symbols, including blackboard bold ("hollow") and Greek letters, should never be italicized. "Italicize math symbols" is a good rule of thumb but the full rules are more complex. See the style guides for major math journals for some examples.
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September 15th, 2014, 02:05 AM   #4
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I'd say, Iff it's in italics, you can change the definition in the article/your work. You can define $\displaystyle A = {1,2,3}$ if you like but $\mathbb{R}$ are the reals.
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September 15th, 2014, 06:35 AM   #5
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My personal uninformed opinion is that Roman letters used to denote mathematical objects are italic to further distinguish them from regular text. For example, if you have a variable $\displaystyle a$ in an equation, and you're mentioning it in a body of text, you put it in italics to distinguish it from the article "a". There is no need to do this with $\displaystyle \mathbb{N}$, $\displaystyle \mathbb{R}$, etc.
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