query: there is no entire function f(z) which verifies that |f(z)| > |z| for every z ∈ C.
positive_passages.docid: 28620
positive_passages.text: Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
negative_passages.docid: 56567
negative_passages.text: Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 84206
negative_passages.text: How do I show that if $f$ is entire and $\{\lvert f(z)\rvert < M\}$ is connected for all $M$, then $f$ is a power function?
negative_passages.docid: 135129
negative_passages.text: Proving an entire  function which misses a ball is constant
negative_passages.docid: 65548
negative_passages.text: Prove if f(z) is entire function s.t $|f(z)|\leq M|z|$ then $f(z)$ Is polynomial of degree $1$
negative_passages.docid: 14994
negative_passages.text: Showing a function $f$ cannot be surjective
negative_passages.docid: 69804
negative_passages.text: Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
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: 20955
negative_passages.text: Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
negative_passages.docid: 81758
negative_passages.text: Suppose an entire function $f$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero.
negative_passages.docid: 106768
negative_passages.text: Recognizing that a function has no elementary antiderivative
negative_passages.docid: 58178
negative_passages.text: Property of Entire Functions
negative_passages.docid: 148512
negative_passages.text: No analytic function $f$ has modulus $|f(z)|=1/\cosh(\Re z)$
negative_passages.docid: 68071
negative_passages.text: If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.
negative_passages.docid: 41201
negative_passages.text: How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
negative_passages.docid: 135524
negative_passages.text: Is $\mathrm{ZFC}^E$ outright inconsistent?