Let the function $f:\mathbb{R}\to \mathbb{R}$ be discontinuous at c. Then the statement: $\mathrm{\forall}\u03f5>0,\mathrm{\exists}\delta \in \mathbb{R},\mathrm{\forall}x\in \mathbb{R}(|x-c|<\delta \phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}|f(x)-f(c)|<\u03f5)$ is false. The negation of the statement: $\mathrm{\exists}\u03f5>0,\mathrm{\forall}\delta \in \mathbb{R},\mathrm{\exists}x\in \mathbb{R}(|x-c|<\delta \phantom{\rule{thickmathspace}{0ex}}and\phantom{\rule{thickmathspace}{0ex}}|f(x)-f(c)|\u2a7e\u03f5)$ is false because whenever $\delta $ is negative, $|x-c|<\delta $ is false. Is anything wrong here? Thank you!