Prove that $\alpha$ is constant on the interval $[0,1]$.
110690
Real Analysis question on FTC, Integral
6100
Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
82405
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $
140300
Does the interval $[0,1]$ contains more real numbers than $(0,2)$?
63889
Prove that if $u_n\rightarrow \infty$ then $\frac{1}{u_n} \rightarrow 0$
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
145632
Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
56127
Prove a function is constant under certain conditions
33786
Proof that a certain fraction is always an integer
39921
show that f is constant on I
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
105768
Proof involving absolute value and maximums
121367
Let $\alpha \in (0,1)$. Find a Borel subset $E$ of $[-1,1]$ s.t. $\lim_{r\to 0^{+}} \frac{m(E\cap [-r,r])}{2r}=\alpha.$
13398
Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
145397
How to prove that for every $i$, $a_i = i$
149827
show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
9696
The interval [0,1] andd [3,5] are equivalent. Is my proof correct?