### Answers (474)

 30 What's the Cartesian Product of $\{x\}$ and $\{x\}$? 29 Can someone give me an example of a challenging proof by induction? 17 How do you understand Infinitesimals? 16 Factorial equation: why does $n!\cdot(n + 2)! = n\cdot(n + 2)!\cdot(n - 1)!$ 14 Solve $\int_0^2 \sqrt{x+\sqrt{x+\sqrt{x+\dotsb}}}\,dx$

### Reputation (11,811)

 +10 difference between hyperplane and plane, examples, pictures +10 If two functions are in Schwartz space,then their convolution is also in Schwartz space +25 Finding the symbol of an differential operator. +10 convergence in $L^p$ implies convergence in measure

### Questions (35)

 14 If $a_nb_n\to 1$ and $a_n+b_n\to2$, do $a_n,b_n\to1$? 10 Rings with 'non-harmless' zero-divisors 7 Characterizing uniform probability on a finite group 7 Intuitive reason why $\sqrt[n]n\to 1$ as $n\to\infty$? 6 How to justify differentiation under the integral in calculation of $\int_0^1\frac{\log(1+x)}{1+x^2}\,\mathrm dx$?

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