Q:

Need a quick clarification about this Coset notation

I'm not looking for an answer to the actual problem, just what this notation could plausibly mean.
Let $G$=$R$ ⊕ $R$, and fix positive real numbers $a$ and $b$. Let $H$=<>. Give a geometric interpretation of the cosets of $H$.
What is that <<$a$,$b$>> ? I've never seen that notation before.
Thanks for any and all input!
Again, thank you all for the input! Much appreciated.

A:

It seems likely that $\langle a, b \rangle$ is intended to denote the ordered pair $(a, b)$, and that $\langle x \rangle$ is intended to denote the subgroup generated by $x$.
Therefore, $\langle \langle a, b \rangle \rangle$ is the subgroup generated by the ordered pair $(a, b)$.

