# Is this notation correct?

I am writing a paper and I have an expression something like this:

$$$$\notag x = \text{large_expression} + \begin{cases} y & \text{if } a<b \\ z & \text{if } a=b \\ \end{cases}$$$$

Will this notation be understood just as well as this more common, undoubtly correct way?

$$x = \begin{cases} \text{large_expression} + y & \text{if } a<b \\ \text{large_expression} + z & \text{if } a=b \\ \end{cases}$$

Note that splitting up $\text{large_expression}$ and $y$/$z$ will hurt the understanding a lot, as well as break the flow of the paper.

• You could make a compromise and let $x =$ large_expression $+f_{a,b}$ where $f_{a,b}$ is what it needs to be depending on $a$ and $b$ – Tobias Kildetoft Oct 16 '13 at 8:29
• Can't you do "large_expression + $x$ where $x = y if...z if...$"? – DanielY Oct 16 '13 at 8:29
• Ok what @TobiasKildetoft offered is simillar but better than mine. Good job :) – DanielY Oct 16 '13 at 8:31
• @TobiasKildetoft I'm afraid that will hurt the understanding. This is for describing a cryptographic scheme, and placing $\text{large_expression}$ and $x$/$y$ further apart from eachother (by introducing another variable or function) will make it harder to see that some events are mutually exclusive, on which the security of the scheme relies. – orlp Oct 16 '13 at 8:33
• The notation you suggest is probably also fine (at least I don't see any way it can be misunderstood). – Tobias Kildetoft Oct 16 '13 at 8:36

Rather than indicator expressions I would suggest the equivalent but somewhat more readable (once you are used to them) Iverson brackets $$x = \text{large_expression} + [a<b]y + [a=b]z\quad.$$ But the solution you suggested is also perfectly understandable an unambiguous, so I don't see much wrong in using it. After all the normal use of the case distinction braces is just after "$=$", which is also in the middle of a syntactic construct; I don't see a fundamental difference when using it after "$+$".
large expression + $y*1_{a<b} + z*1_{a=b}$