gerryliyana Group Title prove that the function f(z) = Re(z) does not have a derivative for any value of z one year ago one year ago

1. gerryliyana Group Title

@phi @Hero @jhonyy9

2. Xavier Group Title

Use the limit definition of the derivative and you have it approaching different values along different lines

3. gerryliyana Group Title

how to prove it using philosophy of course very deeply??

4. sirm3d Group Title

use Cauchy-Riemann conditions for differentiability. $\newcommand {pd}{\partial}\frac{\pd u}{\pd x}=\frac{\pd v}{\pd y},\qquad \frac{\pd u}{\pd y}=-\frac{\pd v}{\pd x}$ given $f(z)=u(x,y) + v(x,y)i$

5. sirm3d Group Title

let $z=x+yi$ $f(z)= \text{Re } z=x+0i$

6. sirm3d Group Title

$u_x=1,v_y=0$ the first condition is not satisfied.

7. gerryliyana Group Title

@sirm3d did you know symmetric tops of molecule??