How would I represent a set of tuples $(a_1,a_2,a_3,…)$, where each element $a_i$ is a positive integer in the interval $1\leq a_i \leq A_i$
The only thing I can think of is defining the set of integers $S_i=\{1\leq k\leq A_i\}$, and then just saying the original set of tuples is, $S_1\times S_2\times S_3\times…$ Where $\times$ denotes the Cartesian product, although this seems like a very messy way to represent this set of tuples, so is there any standard notation or simpler notation for representing a set of tuples like this.
Best Answer
How about $$ \{a\colon\mathbb N\to \mathbb N\mid \forall i\in\mathbb N\colon a(i)\le A_i\}?$$