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Is there a site preference for use of $\Sigma$ ( \Sigma) versus $\sum$ (\sum) for inline summations?

Sum is a larger symbol while Sigma is closer in size to surrounding text, so I prefer the second, but the first use seems more common here.

This is for un-indexed sums, if that makes a difference, but opinions about the general case are also of interest.

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    $\begingroup$ I strongly prefer \sum in all contexts. $\endgroup$ – Brian M. Scott Apr 9 '12 at 21:17
  • $\begingroup$ @Brian: ok, but why? $\endgroup$ – zyx Apr 9 '12 at 21:18
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    $\begingroup$ \Sigma simply looks wrong to me: it’s out of proportion. It looks more like a variable or constant symbol than like an operation. $\endgroup$ – Brian M. Scott Apr 9 '12 at 21:20
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    $\begingroup$ On the other hand, \Sigma aligns with the baseline and the top height of ordinary text (i.e., it fits within the line) while \sum is not aligned. For the same reason, in a paragraph consisting of mostly ordinary-height text, use of \sum will disrupt the vertical spacing between lines, and \Sigma will not. At least for un-indexed sums which are the primary subject of the question. $\endgroup$ – zyx Apr 9 '12 at 21:40
  • $\begingroup$ I don’t want it to align with the ordinary text: that makes it look like a variable or constant name rather than an operation. The disruption in vertical spacing is quite moderate; I don’t find it troublesome. And if for some reason I did, I’d go to display anyway. $\endgroup$ – Brian M. Scott Apr 9 '12 at 21:49
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    $\begingroup$ While I am one of the more active editors, I think this thread should also be taken as a sign to "go easy on editing". It is fine to try to help new users along, try to establish certain standards, and so on. But many of the more experienced users know what they are doing and have their reasons, be it taste or whatever. While editing may be fun, one should always think twice before editing and bear in mind that it need not be appreciated or welcome. $\endgroup$ – t.b. Apr 9 '12 at 22:19
  • $\begingroup$ In the same sense, I recommend using \prod instead of \Pi (id est $\prod$ instead of $\Pi$). $\endgroup$ – user477343 Jun 4 '18 at 5:17
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The symbols have a shared origin, but in contemporary math typesetting they are not the same symbol. They look consistently different: The bottom of a capital Sigma is flush with the baseline of the surrounding text, whereas the bottom of a summation sign descends below it.

Looking at the various versions here, I find that I use this typographic clue to work out whether I'm looking at a summation or a use of Sigma as a variable letter.

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  • $\begingroup$ The alignment of Sigma with the baseline (and the top) of surrounding ordinary text is precisely why I prefer it to Sum. Displayable versions of the small ( math.stackexchange.com/revisions/129785/1 ) and large ( math.stackexchange.com/revisions/129785/2 ) choices are at that posting but the lack of alignment in \Sum also disrupts the line spacing within paragraphs. Use of capital Sigma as a variable name is much less common and would ordinarily be indicated as such ("let $\Sigma$ be a ..."). $\endgroup$ – zyx Apr 9 '12 at 21:37
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    $\begingroup$ You're free to think that a different symbol than the summation symbol would be aesthetically preferable to the summation symbol for expressing a summation, but that doesn't change the fact that what you want to use instead is not a summation symbol. $\endgroup$ – Henning Makholm Apr 9 '12 at 21:40
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    $\begingroup$ It is not a "fact" that a minor typographic difference implies a semantic difference (maybe you also think that boldfacing or having an even larger summation sign would imply a third meaning different from the two you identified?). You may think so but it is hardly a universal convention, and certainly not one that I have ever seen spelled out in any mathematical literature. $\endgroup$ – zyx Apr 9 '12 at 21:44
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    $\begingroup$ @zyx: actually, for the purpose of "Web 2.0" and all that "semantic markup" jazz, you really should not use \Sigma when you mean \sum. Sticklers to the difference between the semantic versus the typographic would instead tell you to redefine \sum to display something that you prefer aesthetically, rather than drop in a symbol with a different semantic meaning. As Mariano alluded to in his answer, the TeX/MathJax backends treat \sum and \Sigma as two different classes of symbols and applies different spacing and limits rules to them. $\endgroup$ – Willie Wong Apr 10 '12 at 8:35
  • $\begingroup$ @Willie: could you explain the effects on semantic markup of using different TeX symbols for the same thing? Say that one uses boldface R and another the Blackboard Bold R to denote real numbers. $\endgroup$ – zyx Apr 10 '12 at 20:44
  • $\begingroup$ @zyx: The semantic difference is more one between \newcommand*\Real{\mathbb{R}} followed by x\in\Real and just writing x\in\mathbb{R}. In the former you separate style/presentation and content. For the purposes of the "semantic web", writing x\in\mathbb{R} and x\in\mathbf{R} are equally bad. $\endgroup$ – Willie Wong Apr 11 '12 at 7:58
  • $\begingroup$ @Willie: sure, in the future people may use a more "semantically marked up" content syntax together with separate control (which can differ for author and reader) over presentation. But this is not made harder if in the present different TeX codes are used for the same semantics, as long as there is relatively little overloading in the lexicon. If mathbb R and mathbf R both are parseable (uniquely or statistically) to RealNumberLine it doesn't matter whether you use one or both. Sigma is more overloaded than Sum but issue you are raising is about unique parsing not unique typesetting. $\endgroup$ – zyx Apr 11 '12 at 9:18
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TeX uses different spacing rules for \sum and \sigma. If you prefer another character to be used for \sum, you can tell TeX to do so and do it properly so that spacing rules are correct. (How to do this is off-topic here, though) I do not know if you can tell MathJax to do this, but I emphatically think that it would be a bad idea to do it anyways.

In any case, for the purposes of this site, personal typographical preferences like this are trumped by consistency. Having everyone start implementing their pet typographical usages in their posts actually diminishes the total value of the content of the site.

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Since I edited your question I guess you deserve my opinion. $\Sigma$ has the problem that it's not in line with the argument of the sumation, yielding $\Sigma f(i)$ whereas $\sum$, as you can see, is centered and underline, so that $\sum f(i)$ looks like a proper summation, where the argument is rather "engulfed" by the sum.

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  • $\begingroup$ While I agree with your preferences, I do think that the edit was completely unnecessary, and I would probably have rejected it for that reason had it come from a low-rep member. $\endgroup$ – Brian M. Scott Apr 9 '12 at 22:01
  • $\begingroup$ @BrianM.Scott I guess we all have our reasons. $\endgroup$ – Pedro Tamaroff Apr 9 '12 at 22:23
  • $\begingroup$ I don't object to the edit, but, not being an expert on TeX or the preferences of users on the site, was curious if there is some consensus I was not aware of when writing the answer. $\endgroup$ – zyx Apr 9 '12 at 22:30
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To me Sigma $\Sigma$ is used when the site has no capability of rendering TeX. In such a case it is a replacement for the sum $\sum$ symbol.

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