# Hello! How to prove the min function is continuous?

1. Oct 27, 2008

### simpleeyelid

Hello!

knowing $$f_{i}:X\rightarrow$$R i=1,2

to show whether $$f_{3}=min{f_{1},f_{2}}$$ is continuous!

Regards

2. Oct 27, 2008

### Office_Shredder

Staff Emeritus
Presumably f1 and f2 are continuous themselves? Is this a homework problem? I'll give you a small hint: work on the points where f1(x)=/=f2(x) and f1(x)=f2(x) separately

3. Oct 27, 2008

### simpleeyelid

yeah, thanks, a lot, I finally find that it is convenient to construct it using the gluing lemma.

4. Oct 29, 2008

### tim_lou

quick solution:

min(f, g) = (f+g)/2 - |f-g|/2