Repeat $\le,\subset$ when starting a new line? My question is very simple. When one sequence of inequalities or inclusions is broken into two or more lines, one should repeat the symbol $\le $ or $\subset$ when starting a new line?
In particular, suppose we want to write $A_1\subset A_2\subset A_3\subset A_4$ in two lines, then the correct notation is
$$A_1\subset A_2\subset $$
$$A_3\subset A_4$$
or the following
$$A_1\subset A_2\subset $$
$$\subset A_3\subset A_4$$
Also, one should write 
$$1\le 2\le $$
$$3\le 4$$
or
$$1\le 2\le $$
$$\le 3\le 4$$
Thank you!
 A: If you don't have the $\le$ or $\subset$ at the start of the second line, it can be quite confusing to the reader as it isn't immediately clear how this line is related to the previous one.  I would tend to use 
$$ \eqalign{ A_1 &\le A_2 \cr
                 & \le A_3 \cr
                 & \le A_4} $$
A: There is nothing like IUPAC for maths. Read recent math books to learn how to write maths now.
My suggestion: the duplication of signs like $\subset$, $\le$, $=$, and so on is useful to make clear that the former line is not an end and the latter is not a beginning, specially when you write maths by hand. Indentations are widely used today, and ending signs are omitted.
A: Note you can hit "edit" to see how things are done in the answers.
To add a bit to Robert's (correct!) answer and Michael's (correct!) comment:
First, don't ever do it the way you did in your question, with two separate displays! You get unpredictable results.
Of course if it's actually $A_1\subset A_2\subset A_3\subset A_4$ that should be just one line. When you do have a chain of inclusions or inequalities or whatever that needs to be broken into several lines you want to use align. And you want to use the & to align the relation symbols. (As in Michael's comment: the two $\le$ are both directly beneath the $=$.)
I think "everyone" agrees so far. Here's my opinion about an issue that comes up. I used to write like this: $$\begin{align}
\left|\int_0^1\sin(t+t^2+t^3+t^4)\,dt\right|&\le\int_0^1|\sin(t+t^2+t^3+t^4)|\,dt
\\&\le\int_0^1|\sin(t+t^2+t^3+t^4)|\,dt
\\&\le\int_0^1|\sin(t+t^2+t^3+t^4)|\,dt
\\&=\int_0^1\,dt=1,\end{align}$$
feeling there was no reason to add another break. These days I tend to feel that if every expression has its own line then every expression has its own line - I write
$$\begin{align}
\left|\int_0^1\sin(t+t^2+t^3+t^4)\,dt\right|&\le\int_0^1|\sin(t+t^2+t^3+t^4)|\,dt
\\&\le\int_0^1|\sin(t+t^2+t^3+t^4)|\,dt
\\&\le\int_0^1|\sin(t+t^2+t^3+t^4)|\,dt
\\&=\int_0^1\,dt
\\&=1\end{align}$$
instead, to be consistent. Easier to read(?), because you know that the next thing is below, not maybe below and maybe to the right, depending.
