# Denseness of a function

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• January 10th 2010, 12:58 AM
Chandru1
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.
• January 10th 2010, 03:17 AM
Shanks
Hint:for a monotonic function, the set of points at which it is not continous is countable.