# Math Help - Denseness of a function

1. ## Denseness of a function

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

2. Hint:for a monotonic function, the set of points at which it is not continous is countable.