Is the following correct?
$$ x_{ap} = x_{ij} \quad \forall a,i \in [1,4]\ \forall p,j \in [1,5] $$
I want to write that $x_{ap}$ is equal to $x_{ij}$. And $i$ and $a$ can only be values between $1$ and $4$. $p$ and $j$ can only take values between $1$ and $5$. Would there be more proper notation?
$[a,b]$ is usually defined as the interval containing all real numbers that are between $a$ and $b$. In this particular context, $\forall a,i\in[1,4]$ wouldn't make much sense if we're speaking about indices that take values over $\mathbb{N}$. A better notation would be, $$\big(\forall a,i\in\{1,\ldots,4\}\big)\big(\forall p,j\in\{1,\ldots,5\}\big)\, :\, x_{ap}=x_{ij}.$$ Or, so as to make it shorter, we may add the condition that $a$ and $i$ can't be $5$, as follows: $$\big(\forall a,i,j,p\in\{1,\ldots,5\}\mid a,i\neq5\big)\, : \, x_{ap}=x_{ij}.$$