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I want to write the statement $A \approx B = C$ in a multi-line format. Is it appropriate to write it as

\begin{equation} \begin{split} A &\approx B \\ &= C \end{split} \end{equation} or does this imply that $A = C$? In other words, do multi-line equations read like a book (left-to-right, top-to-bottom) or like a table?

user2913171
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1 Answers1

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I don't see why not.

We often write

$$\begin{align*} A&=B \\ &\leqslant C \\ &=D\end{align*}$$

and it never means that $A=D$. Only $A\leqslant D$.

But the problem in your case is that if you write

$$\begin{align*} A&\approx B \\ &\approx C \\ &\approx D\end{align*}$$

then you won't necessarily have $A\approx D$ because the relation $\approx$ is not transitive.

We usually reserve this kind of presentation for relations transitive to each other.

That is why we never write

$$\begin{align*} A&<B \\ &=C \\ &>D.\end{align*}$$

which would not make any sense.

E. Joseph
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  • What you are saying makes sense to me. People interpret the multiline sequence as comparing an RHS statement with the RHS of the previous line, and not the LHS. There is another rule here, it seems, because of your example A<B=C>D. Each step of the line is valid, but the multi line syntax is not acceptable. I can see why this example is troublesome, but can you formalize your example to a general statement about what is valid for multi line equations? – user2913171 Oct 28 '16 at 20:37
  • @user2913171 That's what I did when I said your relation $\sim$ needs to be transitive, i.e. $a\sim b$ and $b\sim c$ implies $a\sim c$. – E. Joseph Oct 28 '16 at 20:39
  • I understand the transitive argument for the case where my relation $\sim$ is the same for all lines. My confusion lies when I am using multiple relations, such as your statement $A<B=C>D$ (or my original statement $A\approx B= C$). The relations $<$, $>$, and $=$ are all transitive--so what is the missing rule?

    In any case, you have answered the specific question posed here; I will write a more general question to attempt to make sense of what we are discussing in these comments.

     – user2913171 Oct 28 '16 at 21:34
  • @user2913171 Write a new question if you want, it could be a good idea. What I was trying to explain is that the relation needs to be "transitive with each other". I don't know if it makes much sense said like that, but if you think it could be some use and you write a new question I could try to write it formally. – E. Joseph Oct 28 '16 at 22:40