If $\displaystyle f:\mathbb{R} \to \mathbb{R}$ is an increasing function and $\displaystyle g: \mathbb{R} \to \mathbb{R}$ is a decreasing function then the set $\displaystyle A=\{ x \in \mathbb{R}: f+g \ \textrm{is continuous at} x\}$ is dense in $\displaystyle (\mathbb{R},d)$ where d is euclidean metric.