Meaning of a bracket facing not the interval

Question

What does it mean by $]a,b]$ ? And what is the notation called? First time to for me to see this expression and I cannot get the meaning

Answer 1

We define $[a,\,b]:=\{x\in\Bbb R|a\le x\land x\le b\}$. Endpoints are excluded by reversing a squared bracket's direction or, more commonly, using a round bracket, so $]a,\,b]=(a,\,b]=[a,\,b]\setminus\{a\}$. In the language of topology, it's called either a half-closed or half-open interval (an open interval would lose both endpoints, while a closed interval keeps both).

Answer 2

$]a,b]$ is the interval from $a$ to $b$, including $b$ but not $a$. I think it is more common to write it $(a,b]$, but the notation you show is used as well. We also see $]a,b[$ for the open interval, which includes neither $a$ nor $b$.