What is the meaning of the notation $]1, 1[$?

Question

This may look like a silly question but I am struck in my work with this notation in one of the papers.

What is meant by $]1,1[$ ?

Answer 1

$]a,b[$ is an alternative notation for the open interval that I’d denote by $(a,b)$, i.e., $\{x:a<x<b\}$. Those who use this notation also write $]a,b]$ for my $(a,b]=\{x:a<x\le b\}$ and $[a,b[$ for my $[a,b)=\{x:a\le x<b\}$. Both notations are considered standard, but the $]a,b[$ notation is not common in the U.S.; I believe that it is common in France, however.