Notation for intervals

Solution 1:

As a French student, all my math teachers (as well as the physics/biology/etc. ones) always used the $[a,b]$ and $]a,b[$ (and the "hybrid" $[a,b[$ and $]a,b]$) notations. We also, for integer intervals $\{a,a+1,...,b\}$, use the \llbracket\rrbracket notation (in LateX, package {stmaryrd}): $[[ a,b ]]$.

I have never seen the $\langle a,b \rangle$ notation used for intervals, though (only for inner products or more exotic binary operations).

Solution 2:

The notations $(a,b]$ and $]a,b]$ are both part of ISO 31-11, an international standard for mathematical notation. In the U.S. the former is more common. A few comments comparing the two can be found here, including support for the "French notation" nomenclature.

I have never seen $\langle a,b\rangle$ for closed intervals.