prove that for a continious function if f(q) = 0 for all q where q is rational then all f(x) = 0 when x is real
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
56127
Prove a function is constant under certain conditions
76285
Suppose $f$ is entire and $|f(z)| \leq 1/|Re z|^2$ for all $z$. Show that $f $ is identically $0$.
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
57233
Proof of continuity of Thomae Function at irrationals.
102943
$f(x)=1/q$ for $x=p/q$ is integrable
153043
Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
132478
Prove that continuous functions mapping irrationals to rationals must be constant
53627
Proving continuity of $f$
13927
Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
36983
Does there exist a continuous function such that f(x) is rational for every irrational x, and f(x) is irrational for every rational x?
152347
Proof that a certain entire function is a polynomial
30860
Prove that $f(x)=0$ in $[-1,1]$.
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
147325
Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either
158309
Find a function that is continuous only on rationals