Proving an equality exists in a closed segment of a function.
12632
Universal Chord Theorem
90970
How to prove the line exist?
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
100740
proof of that a continuous function has a fixed point
39921
show that f is constant on I
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
88603
verify equicontinuous functions
150331
Whenever $f=T(x)$ then $f(x) \geq 0$. Prove $T$ is bounded by closed graph theorem.
142459
Continuity of a Function in Terms of Closure and Interior
20863
how do I prove this inequallity?
68700
Proving Two Limits Are Equal to Each Other
121771
Proof $f(x)\equiv 0$
20750
Proving an equality regarding fully independent events
31937
How do I prove equality of x and y?
57938
When do two functions become equal?
104263
How to show that $f'(x)<2f(x)$
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$