Angle brackets for tuples
Some analysts (in a wide sense) write $\langle x,y\rangle$ (angle brackets), for $x$ and $y$ elements of a same set $X$, to denote the ordered pair element of $X\times X$. A more classical (to me) notation is $(x,y)$ (parenthesis), but, if for example $X=\mathbb R$ and $x\leqslant y$, the notation $(x,y)$ may refer to the open interval $\{z\in\mathbb R\mid x<z<y\}$. Hence the bracket notation might have been designed as a way to avoid the confusion. Bourbaki use the notation $]x,y[$ for open intervals and $[x,y]$ for segments. This notation, of frequent use in the mathematical literature written in French (and in others), removes the risk of confusion mentioned above.
I do not know how useful brackets are for objects like $\langle\mathbb Z,+\rangle$, since the objects inside the brackets are of a different nature.