On my mathematical notation

As you do things over and over, you tend to find shortcuts. In this post, I'll list the shortcuts I have found when writing maths. It may be extended in the future. To show the latex source, right click on the math.

\( a = \begin{cases}b\\c\end{cases} \) means "\(a =\) both \(b\) and \(c\), so \(b = c\)".

\(\begin{array}{c}b\\f(n)\\n=a\end{array}\) means the comma separated list \(f(a), f(a+1), f(a+2), \ldots, f(b)\). It mimics the common way to specify ranges in summation. It is ideal for use in tuples, sets and function argument lists.

I also like to vary the indentation, kind of like you do when programming. The basic rule is that you increase indentation by one step to indicate that the block on that level belongs to the line above it. I use it frequently to isolate the value of variables from the expression that they belong to:
\[
F = ma\\
\quad m = 4 \,\mathrm{kg}\\
\quad a = 10 \,\mathrm{m}/\mathrm{s}^2\\
F = 40 \,\mathrm{N}
\]