I'm trying to understand a prove and struggling with the following introduction of a Notation:
"Furthermore, let us introduce the notation $[k,l) = \{k,k+1,\dots,l-1\}$", with the numbers taken modulo $n$, and no number occurring more than once. In particular, $[k,k) = \mathbb{Z}/(n)$ for every $k$."
If I choose $n=4$, then $[2,7) = \{0,1,2,3\}$ and $[2,4) = \{2,3\}$. But why is $[3,3) = \mathbb{Z}/(4) = \{ 0,1,2,3 \}$?
(Source: https://books.google.de/books?id=ButlynVk25MC&pg=PR7&lpg=PR7#v=onepage&q&f=false – Problem 7: African Rally)
Taladris's comment is a good explanation, but to perhaps make things more obvious: if we let $k=4$ we have $[4,4)$ as the notation, which we understand expands to $[4,3]\mod 4$. However, we're also working modulo $4$, so applying the standard notation that $4 \equiv 0 \mod 4$ we now have $[0,3]$. So this yields the set $\{0,1,2,3\}$ as required.
You note in your own comment that you're starting at a point and could not move and still reach that point. Well yes, but actually you're not trying to reach the point you start from, you're trying to reach the point immediately "behind" it (speaking rather loosely) without being allowed to move backwards.