I have a question regarding this graph, for $f(x)=x-[x]-\dfrac{1}{2}$, where $[\cdot ]$ denotes the greatest integer function. My question is about the graph, why does the first slop has an open circle at $(-3,-0.5)$? shouldn't it be a close circle since $f(-3)=-3-[-3]-\dfrac{1}{2}=-0.5?$
It looks as if your software may be treating $[n]=n-\frac12$ for integer $n$
That would be halfway between $\lim\limits_{x \to n^{-}} [x]=n-1$ and $\lim\limits_{x \to n^{+}} [x]=n$, but it is not a common usage of a floor function aimed at producing integers