Considering a finite sequence of real numbers $x_0, x_1, ..., x_n$, which has no particular order, could I write a single statement that says the difference between any two elements of the sequence is less than some real number $y$?
In other words, can I write all of the following inequalities as a single statement?
$|x_0 - x_1| < y, |x_0 - x_2| < y, ..., |x_0 - x_n| < y, |x_1 - x_2| < y, |x_1 - x_3| < y,...,|x_1 - x_n| < y,.., |x_{n-1} - x_n| < y$
EDIT: More specifically, I'm looking for a single inequality, involving $y$ and some linear combination of $x_0, x_1, ..., x_n$, that is only true if the above list of inequalities is true.
Sure, how about "$|x_i-x_j|<y$ for all $i$ and $j$". Or if you want to be more formal; $$(\forall i,j\in\{0,\ldots,n\})(|x_i-x_j|<y).$$ Alternatively, you could write $\max_{i,j}\{|x_i-x_j|\}<y$.