Is it necessary that either $f(x) \leq 0$ for all $x$, or, $f(x) \geq 0$ for all $x$
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
21954
A question about $f(x)\equiv 0$
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
31846
Does $\neg(x > y)$ imply that $y \geq x$?
124139
If $f(f(x))$ is a linear function, must $f(x)$ be linear?
52880
Intuition: If $a\leq b+\epsilon$ for all $\epsilon>0$ then $a\leq b$?
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
86518
Does $X$ have a lower bound?
42853
If $f \geq 0$ is continuous and $\int_{a}^{b} f(x) \, dx = 0$, then $f =0$
59063
$f(f(x))=f(x)$ question
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
128171
Proof for Integral Inequality $|\int f| \le \int |f|$ - is it sufficient enough?
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
121771
Proof $f(x)\equiv 0$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
148470
bound of the function
1307
Infimum and supremum of the empty set