Illustration of the discontinuity of the function f:R→R:x↦{sin⁡(1x)x≠00x=0{\displaystyle f:\mathbb {R} \to \mathbb {R} :x\mapsto {\begin{cases}\sin \left({\tfrac {1}{x}}\right)&amp;x\neq 0\\0&amp;x=0\end{cases}}}. The graph is shown together with the points (xn,f(xn)){\displaystyle (x_{n},f(x_{n}))} with xn=1π2+2nπ{\displaystyle x_{n}={\frac {1}{{\frac {\pi }{2}}+2n\pi }}} (green) and the point (0,f(0)){\displaystyle (0,f(0))} (orange).
Own work
Stephan Kulla (User:Stephan Kulla)