Let $TD$ be an integer (That is, $TD \in \{ 1,2,3,4,\dots \}$). I am looking at the following statement:
If $TD$ is even, the (solution) is given by $$ \forall \frac{TD}{2}\in \mathbb{N}: x_i^* = 1 - \sum_{t=1}^{TD} \delta_i^{t-1}\delta_j^t + \sum_{t=1}^{TD}\delta_i^t\delta_j^t $$
The book am I looking at this in actually uses $\frac{TD}{2}$ for the upper limit of the sum. That is, if $TD = 2$, then the sum is from $1$ to $1$. If $TD=4$ then the sum is from $1$ to $2$
I am wondering if this is proper notation in some field (which I'm considering a possibility since they are defining the equation "$\forall \frac{TD}{2}$") or if there is just a typo or something (there are other typos in the section, so it is very possible).
The reason why I am considering it not being a typo is because I don't know if saying $\forall \frac{TD}{2}$ redefines $TD$ or something... I am looking for an explicit change in usage somewhere or an aside, but so far I don't see one.
It's also a ~20 year old book, so that might have something to do with this.
Thanks.