query: Prove that this function is not integrable: $f(x)$ is $1-x$ for $x$ rational, and $1/x$ for $x$ irrational
positive_passages.docid: 21843
positive_passages.text: Proving a function is not Riemann integrable
negative_passages.docid: 127538
negative_passages.text: Show $f(x)=x\ln x$ is not uniformly continuous
negative_passages.docid: 83825
negative_passages.text: $f^{-1}([-\infty,r))$ measurable for all rational numbers $r$
negative_passages.docid: 62947
negative_passages.text: If $f(x)$ is equal to $x$ or $1-x$ when $x$ is rational/irrational, then $f$ is continuous only at $x=1/2$
negative_passages.docid: 124061
negative_passages.text: Prove the reciprocal of a function is integrable if it is bounded
negative_passages.docid: 90533
negative_passages.text: Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
negative_passages.docid: 91775
negative_passages.text: Show that $\int_0^1 f^2(x)dx\geq 3$, if $f:[0,1]\to \mathbb{R}$ is an integrable function s.t. $\int_0^1 f(x)dx=\int_0^1 xf(x)dx=1$
negative_passages.docid: 127868
negative_passages.text: If $f$ is nonnegative and integrable then $F(x) = \int_{-\infty}^x f$ is continuous.
negative_passages.docid: 61267
negative_passages.text: List of functions not integrable in elementary terms
negative_passages.docid: 34542
negative_passages.text: If $f$ is integrable then $|f|$ is also integrable
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: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
negative_passages.docid: 53191
negative_passages.text: Showing a meromorphic function is rational
negative_passages.docid: 18825
negative_passages.text: Integrable but not differentiable function
negative_passages.docid: 53497
negative_passages.text: Prove that the function is continuous and differentiable (not as easy as it sounds imo)
negative_passages.docid: 138054
negative_passages.text: Proving that $\int_0^1 f(x)e^{nx}\,{\rm d}x = 0$ for all $n\in\mathbb{N}_0$ implies $f(x) = 0$
negative_passages.docid: 111470
negative_passages.text: Proof of differentiability of $f(x)$