Showing that $f(x) = g(x)$ $\forall x$ if $f(r) = g(r)$ for all rationals $r$
2321
Can there be two distinct, continuous functions that are equal at all rationals?
48780
How t show $f=g$ almost everywhere
56967
Show that $ f^2 − g^2 = C $ for some real constant C
100845
How to prove that $G(x)=ax+b$ is a one-to-one correspondence where $a\neq0$ and $a,b\in\mathbb{R}$.
84143
Given any function $g(x): \mathbb{R} \rightarrow \mathbb{R}$, find a function $f(x)$ such that $f(f(x)) = g(x)$.
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
102553
How to show that $f(z) = f(i)$
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
110313
Prove that $\gcd(f(x),g(x)) = 1$.
118348
Let $x$ be transcendental over $F$. Let $y=f(x)/g(x)$ be a rational function. Prove $[F(x):F(y)]=\max(\deg f,\deg g)$
145397
How to prove that for every $i$, $a_i = i$
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $