I have a set with the notation $\mathbb{M}_{b}^{p}$ where $b,p$ define some kind of attribute of that set.
The union of the sets with all possible values for $b,p$ is easy:
$\bigcup_{b=0}^{\infty} \bigcup_{p=0}^{\infty} \mathbb{M}_{b}^{p}$
However, how do I notate the intersection?
I guess this is wrong:
$\bigcap_{b=0}^{\infty} \bigcap_{p=0}^{\infty} \mathbb{M}_{b}^{p}$
because it would first take the intersection with $p$ and then intersect the result with $b$.
This one is better:
$\bigcap_{b,p=0}^{\infty} \mathbb{M}_{b}^{p}$
But now I fear that it is unclear that I want all possible combinations of $(b,p)$ and not just $(0,0)$, $(1,1)$, etc.
So, how do I notate the intersection correctly?
Update: Just an example of how $\mathbb{M}_{b}^{p}$ could be defined, in case the notation is confusing:
$\mathbb{M}_{0}^{0} := {6}$ , $\mathbb{M}_{0}^{1} := {7}$ , $\mathbb{M}_{1}^{0} := {7}$ , $\mathbb{M}_{1}^{1} := {8}$