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Often when creating reports for labs or something like that I find myself writing something like:

QUESTION DESCRIPTION

Question is:

As the formula is often on its own line, once I say "(...) where e (...)" should the 'W' be capital or lowercase? What I mean is that changing from formula back to text is like starting a new line.

Additional question (if I am allowed):

In the preamble to the formula "(...) for any real number x (...)", should I put a colon (:), a comma (,), a dot (.), or nothing (as it is in this question)?

The possibilities are

  • "(...) for any real number x, eix (...)", f(x)=(z-y)e0.01-0.01x+y

  • "(...) for any real number x: eix (...)",

  • "(...) for any real number x. eix (...)"

  • and as it is in the question (no punctuation after "x").

Note: In wikipedia they use a dot.

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  • Could you write out the possibilities in full with regard to the colon? I can't visualise what you mean. Commented Jul 18, 2015 at 23:52
  • @chaslyfromUK First, let me thank you for the quick answer, I will accept it as soon as I am allowed to. Possibilities are "(...) for any real number $x$, e^{ix} (...)", "(...) for any real number $x$: e^{ix} (...)", "(...) for any real number $x$. e^{ix} (...)" and as it is in the question. In wikipedia they use dot.
    – Hans
    Commented Jul 18, 2015 at 23:54
  • 1
    I've edited that into your question to make it more readable.. Can you check I've done it right? Commented Jul 19, 2015 at 0:13
  • It would be very helpful if you could give the URL of the Wikipedia entry. That way we could see the whole thing. Commented Jul 19, 2015 at 0:17
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    @Hans: For your context, one could as well be dealing with a line of computer code as an equation. And given that in some computer languages, a comma is a "syntactically" significant character, it wouldn't be a very wise choice if you want a generic approach. But there isn't really a "right" here - just different styles (possibly supported by different style guides). Personally I think you've asked on the wrong site - I'm sure the guys over at SO Tex would be more familiar with the issue, and more likely to share a consensus over "best practice". Commented Jul 19, 2015 at 2:19

3 Answers 3

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Personally (and in accordance with the conventions that I've seen in published works), I'd write it as follows:

Euler's formula states that, for every real number~$x$,

\begin{equation}
  e^{ix} = \cos x + i \sin x,
\end{equation}

where $e$~is the base of the natural logarithm.

The philosophy is that the equation is a statement, part of the sentence. You should therefore punctuate it in the same way as you would were it run in with the text.

See also this MathOverflow thread on the subject. In particular, this answer has a few examples in this style.

Here's another good answer on TeX.SE.

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  • Note also the ties (~)—they're important!
    – wchargin
    Commented Jul 19, 2015 at 4:54
  • Is that only to don't "leave the $x$" alone?, wow, I didn't know that was a convention.
    – Hans
    Commented Jul 19, 2015 at 4:56
  • Use a thin space (\,) to separate the punctuation from the math: \sin x \,, Commented Jul 19, 2015 at 5:46
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for any real number $x$

$e^{ix}=\cos{x}+i\sin{x}$

where $e$ is the base of the natural logarithm (...)"

I can see no reason for capitalising 'w' in that situation - a newline doesn't signal the start of a new sentence. I would find it very confusing if you capitalised it.

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Only if it's two different sentences. If the formula is just the subject or the object of the same sentence then there should be no need to capitalize the next word. (unless it is a proper noun or a quote or something like that).

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