query: Does entire and v>0 implies f is constant?
positive_passages.docid: 114245
positive_passages.text: What might I use to show that an entire function with positive real parts is constant?
negative_passages.docid: 136011
negative_passages.text: Must $f$ be continuous?
negative_passages.docid: 141863
negative_passages.text: If the imaginary part of an entire function is never zero, the function is constant
negative_passages.docid: 82001
negative_passages.text: How to prove the function is a constant
negative_passages.docid: 5416
negative_passages.text: How does one prove if a multivariate function is constant?
negative_passages.docid: 132113
negative_passages.text: Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?
negative_passages.docid: 91352
negative_passages.text: If $\Re(f)$ is bounded then f is constant.
negative_passages.docid: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
negative_passages.docid: 150502
negative_passages.text: If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$
negative_passages.docid: 154034
negative_passages.text: Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
negative_passages.docid: 138544
negative_passages.text: For which values of $x$, will $f (x) . f '(x) < 0$?
negative_passages.docid: 75390
negative_passages.text: How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
negative_passages.docid: 93270
negative_passages.text: is that function must be constant under the following conditions
negative_passages.docid: 33247
negative_passages.text: Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
negative_passages.docid: 64650
negative_passages.text: If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
negative_passages.docid: 114179
negative_passages.text: If $Var(X)=0$ then is $X$ a constant?
negative_passages.docid: 39921
negative_passages.text: show that f is constant on I