How to write $b$ between $a$ and $c$ formally? How to write $b$ between $a$ and $c$ formally ? I mean it could be 

1) $a&lt;b&lt;c$

or

2) $a&gt;b&gt;c$

but I want to leave it in the middle which one it is.

If I use the sandwich theorem for instance I think a notation for this might be usefull.
$$\min\{ a,c \} &lt;b &lt; \max\{ a,c \}$$

or 
$$(b-c)(b-a) &lt;0 \,.$$
$a&lt;b&lt;c$ and $a&gt;b&gt;c$ are not the same (I assume that was a typo). 

But, $a&lt;b&lt;c$ and $c&gt;b&gt;a$ are the same things. In this case, both notations work. The first one looks cooler and easier to understand (to me). By the way, Also, you need to make sure that the inequalities are strict, e.g. $1&lt;1&lt;1$ is false, but $1 \leq 1 \leq 1$ is true.