Find the range of $f(x)=x-[x]$ ,where $[x]$ stands for greatest integer function. The answer could be any of these $[0,1]$ or $[0,1)$ or $(0,1)$ or $(0,1]$. Can someone help with this?
2026-04-23 14:56:53.1776956213
Range of greatest integer function.
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Notice that for$ x=k\in \mathbb {Z}$ , we have $x-[x]=0$.
On the other hand if $k<x<k+1$ then $0<x-[x]=x-k<1$
Therefore the range of $x-[x]$ is $[0,1)$