This comes up a lot when discussing Grassmannian manifolds, or at least it seems to me. Anyway, if someone writes something like $$\mathbb{RP}^n = O(n+1)/O(n)\times O(1) $$ does the right hand side mean $$O(n+1)/ \ [O(n)\times O(1) ]? \quad or\quad [O(n+1)/O(n)]\times O(1)? $$ Does it not matter in general? I.e. are the two alternatives I gave in general isomorphic (as differentiable manifolds or otherwise)?
I know that for numbers $a/bc$ means $a/(bc)$ (PEMDAS), but generally speaking it's best not to use atrocious notation like that for which one has to think about how to interpret it.