# At what point is f(x) = x - [x] discontinuous?

Apr 14, 2015

I assume that $\left[x\right]$ is the greatest integer in $x$ also known as the floor function.

$x - \left[x\right] = 0$ for integer $x$ and it is the decimal part of $x$ for non-integers.

As a consequence of that, the graph of $x - \left[x\right]$ consists of line segments joining points $\left(n , 0\right)$ with $\left(n + 1 , 1\right)$. Closed at the first point and open at the second.

$x - \left[x\right]$ is continuous at non-integers (locally linear) and continuous from the right at integers.

I found this online:
at imageshack.com