30 Fermat's Last Theorem and Faltings' Theorem. 20 How does one evaluate $1+2-3-4+5+6-7-8+\cdots+50$? 9 Proof that the number of proofs is countably infinite 9 Let $f\in L^1(\mathbb R)$ and let $F,G:\mathbb R\to\mathbb R$ be the functions defined by: … 7 $\bigcap I_\gamma$ unbounded if $I_0 \supset \cdots \supset I_{\gamma}\supset \cdots$ are unbounded

### Reputation (6,965)

 +10 Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem +10 Linear order of the quotient generated from Vitali relation implies non-measurability of subset of reals +10 Linear order of the quotient generated from Vitali relation implies non-measurability of subset of reals +10 Proving the inequality of given function

### Questions (36)

 5 Linear order of the quotient generated from Vitali relation implies non-measurability of subset of reals 5 Prove that $\lim\limits_{x\to\infty}\frac1x=0$ 4 Is $c + \sin c + \sin\sin c + \sin\sin\sin c + \cdots$ convergent? 4 differential-equation with trigonometric functions 3 Symmetry of second derivative - Sufficiency of twice-differentiability

### Tags (159)

 66 elementary-set-theory × 50 29 algebra-precalculus × 23 65 calculus × 64 28 summation × 6 60 real-analysis × 50 25 elementary-number-theory × 6 38 limits × 46 24 proof-verification × 36 36 number-theory × 4 24 set-theory × 13