Show $f=g$ for all reals given $f=g$ for all rationals ( epsilon-delta continuity)
2321
Can there be two distinct, continuous functions that are equal at all rationals?
105455
Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
75479
Proving that this function is continuous on $G\times G$
125682
Proof verification: the product of two continuous functions is continuous
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
34940
Continuity of $f(x) = x^n$
109570
How to show that the set of points of continuity is a $G_{\delta}$
102553
How to show that $f(z) = f(i)$
151493
Using $\epsilon$-$\delta$ to show a property of a function
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
139979
Proof there is a rational between any two reals
128911
Continuous extension of a real function
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const
56567
Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
12107
How is the epsilon-delta definition of continuity equivalent to the following statement?