Math symbol for saying that $a>b \to x>y$ as well as $a=b \to x=y$ I want to state the following:
$a>b \rightarrow x>y\\
a=b \rightarrow x=y\\
a<b \rightarrow x<y$
as short as possible. I don't like the redundancy in having 3 lines looking very equal, and thought it could be stated using a mathematical symbol (I cannot yet come up with) in a one-liner.
I have thought of something like this:
$sign(a-b) = sign(x-y)$ but it will cause some confusions for the 0-case.
 A: I think I've seen something like this in the past:
$$
a \gtreqqless b \implies x \gtreqqless y
$$
but you probably ought to explain to readers what it means
the first time you use it in any document.
The idea (I think) is that this is more like the use of multiple coordinated
$\pm$ signs than like the usual $\geq$ or $\leq$.
The Mathjax for this is \gtreqqless. There's also \lesseqqgtr, which
produces $\lesseqqgtr$.
A: Note that if $a,b$ are symmetric and $x,y$ are symmetric, and $<$ is a strict total order (such as the comparison relation on real numbers), then your three statements are equivalent to:
$\def\eq{\Leftrightarrow}$
$\def\imp{\Rightarrow}$
$\def\rr{\mathbb{R}}$

$a < b \eq x < y$.

Here by symmetry I mean that:

$( a < b \eq x < y ) \imp ( b < a \eq y < x )$.

Symmetry often holds in contexts where such kinds of comparisons make sense.
For example:

$\forall a,b \in \rr\ ( a < b \eq a^3 < b^3 )$

is equivalent to:

$\forall a,b \in \rr\ ( ( a < b \imp a^3 < b^3 ) \land ( a = b \imp a^3 = b^3 ) \land ( a > b \imp a^3 > b^3 ) )$.

