How can I "prettify" complex equation systems in MathJax / $\TeX$?

Question

I have the problem that I want to use a (long) equation chain to show the relation between two statements.

How do I do that?

Answer 1

The simplest way is to just use $<YOUR EQUATION HERE>$ like in this example $f(x)=x^2$ ($f(x)=x^2$). This is also called text-mode math, because things like $\bigoplus_a^b$ put the $a$ and $b$ on the right side instead of above and below. This is what you should use whenever you just need a simple equation "on the go".

The next more "fancy" way is to use "displaymode", which can be used by $$<YOUR EQUATION HERE>$$, example: $$f(x)=x^2$$ It is also possible to use \begin{equation}f(x)=x^2\end{equation} (\begin{equation}<YOUR MATH STUFF HERE>\end{equation}) if you prefer the more $\LaTeX$ way of doing things. You should use this mode whenever you have some result that you want to emphasize.

The last interesting tool is "aligned displaymode". \begin{align}f(x)&=x^2\\&=x^3\end{align} is an example for this mode. You can use it via

\begin{align}
<LEFT-SIDE> & <RIGHT-SIDE> \\  % this would be "f(x) & = x^2"
[<LEFT-SIDE>] & <RIGHT-SIDE>\\ % this would be "& = x^3"
[<LEFT-SIDE> & <RIGHT-SIDE>]
\end{align}