# Subsets - analysis

1. Feb 6, 2010

### Fairy111

1. The problem statement, all variables and given/known data

I need to find out whether the subset Re(real no's) of complex no's is open, closed or neither.

2. Relevant equations

3. The attempt at a solution

Im not really sure how to begin this...any help please?

2. Feb 6, 2010

### HallsofIvy

Staff Emeritus
Let x be any real number and consider a neighborhood of it in the complex numbers: $\{z | |z- x|< \delta\}$. Does that contain any non-real numbers?

3. Feb 7, 2010

### Fairy111

yes i think it does contain non real numbers, so this would imply that it is an open subset?
how would i go about sketching it?