# Math Help - tough continuity problem need help

1. ## tough continuity problem need help

g(x)=0 if x is rational
g(x)=x if x is irrational

for what values of x is g continuous?

2. Originally Posted by myoplex11
g(x)=0 if x is rational
g(x)=x if x is irrational

for what values of x is g continuous?
Have you ever heard of "Dirichelt" function?
Same idea.

The limit that we approach a point bt rationals needs to be the same as we approach the limit by irrationals. In that case $x=0$ is the only continous point.
Look Heir

3. i understand why it is continous a x=0 but i need to justify this mathematically

4. Originally Posted by myoplex11
i understand why it is continous a x=0 but i need to justify this mathematically
Choose any $\delta>0$ and set $\epsilon=\delta$, then $|g(x)-g(0)|<\delta$ whenever $|x|<\epsilon$,
hence $g(x)$ is continuouse at $x=0$.

RonL