I want to show that $\nabla\times (f\nabla g)=\nabla f\times \nabla g$.
We have that $f\nabla g=f\sum\frac{\partial g}{\partial x_i}\hat{x}_i$, therefore we get $\nabla\times (f\nabla g)=\nabla\times \left (f\sum\frac{\partial g}{\partial x_i}\hat{x}_i \right )$.
Is it correct so far? How could we continue?
https://www.youtube.com/watch?v=GiPe1OiKQuk
alot of people make fun of Rumsfeld for the "unknown unknowns", but i'm wondering how a person like him would start to try to get his hands around the "unknown unknown". With known unknown, you can probably setup a strategy to explore the unknown.
My...
We construct a sequence $S$ of distinct positive integers as follows
1) the sequence $S$ starts as $1,2,3$
2) If and only If $x,y$ are in the sequence and $ x^2 + y^2 > 3 $ Then $x^2 + y^2 $ is also in the sequence.
3) the sequence is strictly increasing.
4) the sequence is completely determi...
