Good day, we are currently covering basic principles for algorithm optimisation and we were tasked with explaining the following problem.
Assume $x,y \in \Bbb R$. How much can the following two integers differ:
$\lfloor x \rfloor - \lfloor y \rfloor$ and $\lfloor x-y \rfloor$
These can clearly be equal but I am not quite sure how to explain or approach the explanation of how they differ.
They can differ by at most the difference between the integer parts of $x$ and $y$ but I do not think that this is enough.