This is a very simple question, but i don't have a clue how to prove this..
Let $[x+y]$ denote $x+y$ and $(x)$ be a fractional part of $x$
Suppose $x$ is an irrational number and $n$ is an integer.
Let $\delta \in (0,\frac{1}{2}\min\{(nx),1-(nx)\})$
Here, how do i prove that $(n[x-\delta])=(nx)-(n\delta)$ and $(nx)<(n[x+\delta])$?
Thank you in advance