Prove the following function is continuous at all irrational points
71877
Continuity of Popcorn Function (Thomae's Function)
30478
How to prove that a number is irrational
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
62048
Proving a Lipschitz function is continuous
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
53627
Proving continuity of $f$
18222
Set of continuity points of a real function
150554
proof that $f'$ is continuous at $a$
31744
Proving that there is an irrational number between any two unequal rational numbers.
72044
prove $x \mapsto x^2$ is continuous
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
151427
f, g continuous for all rationals follow by continuous on all reals?
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
4381
Proof that the set of irrational numbers is dense in reals
111094
Help with proving that $\pi$ is irrational
52486
Is there a function that is contiunous at all the rationals, and discontinuous at all the irrationals?
5881
$\sqrt x$ is uniformly continuous