Show that there exists $a,b\in\mathbb{R}$ such that $f(x)=ax+b$ for all $x\in\mathbb{R}$.
62110
Proving a function $\frac{1}{2y}\int_{x-y}^{x+y} f(t) dt=f(x)$ is a linear polynomial
2575
Showing that $\mathbb{R}$ is connected
57649
Prove that for every $f$, a bilinear form, there exists a basis ${v_1,...,v_n}$ so that $f(v_i,v_j) = -f(v_j,v_i)$
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
58189
Bolzano-Weierstrass Theorem Proof Abbott (Ax. of Choice)
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
61640
Prove c exists for f:[0,1] -> R
12596
Show that $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in R[x]$ is nilpotent iff $a_0,a_1,a_2,\ldots,a_n$ are nilpotent
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
75266
$f(a+b)=f(a)+f(b)$ but $f$ is not linear
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
105769
Prove that $\exists a, b\in(0,1)$ such that $\int_0^{a} xf(x)dx=0\text{ and }\int_0^bxf(x)dx=\frac{b^2f(b)}{2}.$
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$