Tuple definition Is it correct?
$S=\{\langle t,h\rangle:t\in\{0,\Delta t,2\Delta t,\cdots,24\},h\in\{0,\Delta h,2\Delta h,\cdots,H\}\}$
I would like to say that $S$ is a 2-tuple. The first tuple can vary from $0$ to $24$, with $\Delta T$ step, and the second one can vary from $0$ to $H$, with $\Delta H$ step.
 A: $S$ is not a tuple, it's a set of $2$-tuples.
I think what you want to say is that $S$ is a set of ordered pairs ($2$-tuples), each of which has a first entry that can vary from $0$ to $24$ in steps of length $\Delta t$; and second entry that can vary from $0$ to $H$ in steps of length $\Delta h$. As written, it would only make sense if $24$ is evenly divisible by $\Delta t$ and $H$ by $\Delta h$; that is, if and only if there exist integers $k$ and $\ell$ such that $24 = k\Delta t$ and $H=\ell\Delta h$.
If the latter is not the case, then I would say that the first entry will take the values $k\Delta t$ with $k=0,1,2,\ldots,\lfloor\frac{24}{\Delta t}\rfloor$, and the second entry will take the values $\ell\Delta h$ with $\ell=0,1,2,\ldots,\lfloor\frac{H}{\Delta h}\rfloor$. 
Note, however, that $S$ is a set of tuples (not a tuple), and it is the first/second entry of the elements of $S$ that we are describing, not a "first tuple" and "second tuple": the elements of $S$ are themselves not ordered, so it doesn't make sense to talk about a "first tuple" and a "second tuple", when $S$ is a set.
