Where can I find the official rule for multi-line expressions?

Question

Consider this simple exercise:

$$1+1+11+1+1 = 15\tag{A}$$

But what if it were a very long expression? Let's assume that it is, then

$$\begin{equation*} \begin{split} 1+1+\; & \\ 11+1+1 &= 15 \end{split} \end{equation*}\tag{B}$$

would still be valid.

But would

$$\begin{equation*} \begin{split} 1+1+1\; & \\ 1+1+1 &= 15 \end{split} \end{equation*}\tag{C}$$

(where the $11$ is split between lines) be valid too? I'm sure it won't be, but I need the official place to look it up.

My question is: where can I find the right/official(!) way to split a long algebra drill?

Answer 1

There's no "official" rulebook for how to write mathematics. Arguably, anything is fine as long it is

• already commonly accepted, or
• sufficiently clear from context, or
• explained by the author beforehand

but in any situation, it would be advisable not to do anything that would surprise your readers too much (e.g., using the symbol $\large \texttt6$ for a variable). Your case $\text{C}$ falls into this category: you could explain in a sentence leading up to the expression how it should be read, but it is so counter-intuitive that it's just not a good choice.

The only situation I'd consider it acceptable to break a number across lines (and it would still require explanation by the author beforehand) is if the number itself is too big to fit, e.g., the single, $151$-digit number $$1237401579137502793502395782034957203475028 4235284352903232356235823952538 2{\;\small\ddots}\\35723572355 235973475 32823576235803122435723459423284359734580233597200923214\;\;\;$$ The notation with the $\small\ddots$ is what I've seen in this (rare) situation. Mathematica uses it:

Answer 2

Option C is not valid, from either a human or computer viewpoint. A computer might interpret the linebreak as tacit multiplication, in which case we have $1 + 1 + 1 \times 1 + 1 + 1 = 5$, not 15. Or an error message, or other behaviors I can't even predict. Parsers may ignore or conflate certain kinds of whitespace, but to my knowledge no parser is designed to understand a numeric literal broken across lines. Note that this is not the same thing as line wrapping, in which the numeric literal may be displayed as starting on one line and continuing in the next even though there is no spacing character in the numeric literal.

Humans are even more unpredictable than computers. I would interpret the first line as $1 + 1 + 1 = 3$, so on the next line I would be confused to find $1 + 1 + 1 = 15$.

At least Option B makes it clear that the operations are to be continued across the linebreak. We could quibble over the placement of the second plus sign, but even contrarians would understand what you mean even if they pretend not to.

To my knowledge, there are no official rules, though maybe there are some math journals that have their own rules on this sort of thing. But that's why you show a paper to someone else to make sure it makes sense and it looks good.