Update People are downvoting. Maybe I should ask if it is a good idea in the first place to put many equations in one line. I just can't puzzle out something like $a^{-1}(aa^{-1})a = (a^{-1}a)(a^{-1}a) = ee = e = a^{-1}a = a^{-1}(a^{-1}a)a$.
Can you do it? How? Any tips or suggestions for me?

Is there some way to solve the problem of posts that contain way too many equations in one line? Any way to discourage this unconcern for people who are trying to learn the material?

I can update this post if I stumble on any more. An example is the third paragraph on Any Set with Associativity, Left Identity, Left Inverse is a Group. To me at least it's pretty much impossible to read in a reasonable time.

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    $\begingroup$ You appear to object to chained identities like $a=b=c=d$. Putting the argument on one line like this should help frame the goal for most readers; as Euclid said, two things equal to a common thing are equal to each other. It does not promise to speed up the critical thinking behind each link in such chains, but it is an often used device in mathematical exposition. $\endgroup$ – hardmath Dec 23 '13 at 17:17
  • $\begingroup$ @hardmath If 'does not promise to speed up the critical thinking behind each link in such chains' then is it really a good idea or is it better to break up chained identities? Let me know if there are other reasons for it. $\endgroup$ – Group Theory Dec 23 '13 at 17:37
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    $\begingroup$ Your claimed paragraph took me 10 seconds to read...................... What's your solution? $\endgroup$ – Don Larynx Dec 23 '13 at 17:49
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    $\begingroup$ @DavidHolden: Downvoting for Questions on Meta has a different significance than voting on Math.SE. It conveys disagreement with a proposal here, in this case that there should be automated or other ways to prevent people from using chained identities in posts. It's not surprising that community members, regardless of their sense of mathematical aesthetics, would fail to support this proposal. $\endgroup$ – hardmath Dec 23 '13 at 19:32
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    $\begingroup$ fine, I'm just finding my way here. chained identities are not a particular concern, I am happy with the one I have already. as I have written more than once before, I am here to learn some mathematics. when one has a genuine hunger, that makes it easier to tell what foods are nutritious. and as I have also said, I have no problem with downvoting if reasons are given. however that sneaky anonymous downvoting occurs is a fact I have already noted several times in only a few weeks, not merely in my own case. like playground bullying it is something I will oppose wherever I observe it $\endgroup$ – David Holden Dec 23 '13 at 23:10
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    $\begingroup$ People have very different ways of parsing symbols. I voted your question down because you framed your personal problem with reading one-line equations as "unconcern for people who are trying to learn the material". I dislike the hypocrisy of demanding empathy for your problem, but not even admitting the possibility that other people are different. $\endgroup$ – Phira Dec 24 '13 at 22:33
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    $\begingroup$ I would hate to read your example in aligned notation. I DO align chains of equations with longer expressions. $\endgroup$ – Phira Dec 24 '13 at 22:34

This is a space saving device in a way, and a standard notation for a multistep calculation (i.e. not an equation). It is roughly like the following calculation $$ \left(\frac13+\frac12\right)\cdot\left(\frac12+\frac14\right)= \left(\frac26+\frac36\right)\cdot\left(\frac12+\frac14\right)=\frac56\cdot\left(\frac24+\frac14\right)=\frac56\cdot\frac34=\frac58. $$

Are you really suggesting that such a calculation should be split into multiple lines simply so that there would be a single equal-sign on each line? Admittedly that is sometimes an improvement - largely for reasons of lay out. But that wastes quite a bit of space. For example, the above calculation could then look like $$ \begin{aligned} \left(\frac13+\frac12\right)\cdot\left(\frac12+\frac14\right)&= \left(\frac26+\frac36\right)\cdot\left(\frac12+\frac14\right)\\ &=\frac56\cdot\left(\frac24+\frac14\right)\\ &=\frac56\cdot\frac34\\ &=\frac58. \end{aligned} $$

Mind you, I do split a calculation on several lines, if the intermediate steps don't fit into a single line.

On this site saving space is not a major concern. But it becomes so, if you want to fit the calculation on a single slide. Or if you need to squeeze a set of homework problems on a single sheet of paper.

If we did the same in the linked question it would look like $$ \begin{aligned} a^{-1}(aa^{-1})a&=(a^{-1}a)(a^{-1}a)\\ &=ee\\ &=e\\ &=a^{-1}a\\ &=a^{-1}(a^{-1}a)a. \end{aligned} $$ It may be quicker to read. Easier? I don't think so. But it also consumes a lot of space, not to mention keystrokes of TeX-code:-)

The upshot is that this is such a trivial calculation that giving it this much space just feels wrong. Due to its relative unimportance.


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