query: Erroneous argument that every distribution function is left continuous.
positive_passages.docid: 27059
positive_passages.text: Why left continuity does not hold in general for cumulative distribution functions?
negative_passages.docid: 153495
negative_passages.text: Continuous function does not map closed set to closed set
negative_passages.docid: 111907
negative_passages.text: Prove that Cantor function is Hölder continuous
negative_passages.docid: 31548
negative_passages.text: Proof of "every convex function is continuous"
negative_passages.docid: 86327
negative_passages.text: If the absolute value of a function is continuous, is the function continuous?
negative_passages.docid: 83338
negative_passages.text: Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.
negative_passages.docid: 121957
negative_passages.text: Is $p\mapsto \|f\|_p$ continuous?
negative_passages.docid: 3518
negative_passages.text: Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
negative_passages.docid: 58664
negative_passages.text: Proving a function is continuous for a fixed variable
negative_passages.docid: 151410
negative_passages.text: Inequality of continuous functions
negative_passages.docid: 39235
negative_passages.text: Argue that the iterated integral of a continuous function is continuous
negative_passages.docid: 40048
negative_passages.text: Finding the fallacy in this broken proof
negative_passages.docid: 149095
negative_passages.text: $f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
negative_passages.docid: 146707
negative_passages.text: Formally show that the set of continuous functions is not measurable
negative_passages.docid: 108997
negative_passages.text: Continuous functions that attain local extrema at every point
negative_passages.docid: 32571
negative_passages.text: Is the maximum function of a continuous function continuous?
negative_passages.docid: 123972
negative_passages.text: Proving that every function defined on a discrete metric space is uniformly continuous.