I'm working through a proof of correctness for merge sort.
I'm given a loop invariant for a for loop, which makes reference to a subarray $A[p..k-1]$. During the initialization step of the correctness proof, my textbook says "Prior to the ﬁrst iteration of the loop, we have $k=p$, so that the subarray $A[p..k-1]$ is empty".
In other words we're saying $A[p..p-1]$ is empty. Suppose $p=1$, then it's saying $A[1..0]$ is empty. Why is this considered empty? Is it just an axiom that subarray $A[a..b]$ is empty if $a>b$?