query: Prove that $f(z) $ is an odd function when $z \in \mathbb{R}$
positive_passages.docid: 23801
positive_passages.text: A reflection question about a complex function
negative_passages.docid: 54496
negative_passages.text: Showing that $\mathbb{R}$ and $\mathbb{R}\backslash\mathbb{Q}$ are equinumerous using Cantor-Bernstein
negative_passages.docid: 55902
negative_passages.text: Show $R[x]/(x)\cong R$
negative_passages.docid: 45676
negative_passages.text: Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.
negative_passages.docid: 18484
negative_passages.text: Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
negative_passages.docid: 56978
negative_passages.text: How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
negative_passages.docid: 155575
negative_passages.text: Proving a polynomial $f(x)$ composite for infinitely many $x$
negative_passages.docid: 87617
negative_passages.text: Ring of $\mathbb{Z}_2$-valued functions
negative_passages.docid: 152841
negative_passages.text: I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
negative_passages.docid: 102553
negative_passages.text: How to show that $f(z) = f(i)$
negative_passages.docid: 131692
negative_passages.text: How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
negative_passages.docid: 51659
negative_passages.text: If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
negative_passages.docid: 80421
negative_passages.text: Show that $a - b \mid f(a) - f(b)$
negative_passages.docid: 94190
negative_passages.text: Disproving the statement "If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ is not entire.”
negative_passages.docid: 44259
negative_passages.text: Heine-Borel Theorem ($\mathbb{R}^k$) (in ZF)
negative_passages.docid: 157488
negative_passages.text: Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
negative_passages.docid: 75653
negative_passages.text: Prove that $|f ''|\ge 4$