In this snippet from Knuth's Concrete Mathematics,
I'm not sure how we would know the range of $j, k$:
On the left hand side of the above equation, we just are given that $1 \leq j, k \leq 3$ then how do we know that $1 \leq j \leq 3, 1 \leq k \leq 3$?
I assumed that $j$ would increment infinitely from 1 and that $k$ doesn't have a place to begin since there's originally no lower bound...
"$1 \leq j, k \leq 3$" is just questionable notation, it's supposed to be interpreted as "both $j$ and $k$ are between $1$ and $3$ inclusive", so yeah, it does mean $1 \leq j \leq 3 \ \wedge 1 \leq k \leq 3$.
I've seen this more commonly written as $$\sum_{j,k=1}^3 a_jb_k$$ though that's similarly questionable.