$f(x)= 0$ for $x \notin\mathbb{Q}$, and $f(x)=1/q$ for $x=p/q$. Prove: $f$ is integrable
102943
$f(x)=1/q$ for $x=p/q$ is integrable
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
116044
Can one prove $\int f > 0$ for $f > 0$ without Lebesgue integration?
21586
Prob. 7 (a), Chap. 6, in Baby Rudin: If $f$ is integrable on $[c, 1]$ for every $c>0$, then $\int_0^1 f(x) \ \mathrm{d}x = $ . . .
150235
$\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
33247
Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
71953
If $\int_0^1 f x^n dx=0, \forall n \in \mathbb{N} $, then $f\equiv 0.$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
16212
If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) d(x) = 0$ iff $f(x) = 0$
77106
If $f$ is continuous and $g$ is integrable on $[a,b]$, with $g(x) \ge 0$ for all $x \in [a,b]$ ...
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
53432
What is the algebraic closure of $\mathbb F_q$?
82448
Why is $f(x) = x\phi(x)$ one-to-one?