Let $F$ be an infinite field and let $f(x) ∈ F[x]$. If $f(a) = 0$ for infinitely many $a ∈ F$, show that $f = 0$.
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
74583
Prove that $f'(0)=L$.
105700
Proving $\,f$ is constant.
133386
If $f$ is entire and $\lim_\limits{z\to\infty} \frac{f(z)}{z} = 0$ show that $f$ is constant
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
132824
Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
21954
A question about $f(x)\equiv 0$
130161
Showing that if $\lim_{x\to\infty}xf(x)=l,$ then $\lim_{x\to\infty}f(x)=0.$
97904
Example of infinite field of characteristic $p\neq 0$
44129
If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
145424
If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.
16212
If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) d(x) = 0$ iff $f(x) = 0$
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.