1. ## Discontinuous Functions

Hey for some reason I'm really struggling with this one problem--

Q: If f and g are both not continuous at a, then f+g is not continuous at a. Prove or Disprove.

2. Originally Posted by johnlaw
Hey for some reason I'm really struggling with this one problem--

Q: If f and g are both not continuous at a, then f+g is not continuous at a. Prove or Disprove.

How about taking $a=0, ~ f(x) = \frac{1}{x}, ~ g(x) = -\frac{1}{x}$?
How about taking $a=0, ~ f(x) = \frac{1}{x}, ~ g(x) = -\frac{1}{x}$?
True, so define $f(x)=\begin{cases} 0 & \mbox{if} \quad x=0 \\ \frac{1}{x} & \mbox{if} \quad x\ne0 \end{cases}$. Then, $f,-f$ are both not-continuous at zero but $f+-f=0(x)$