Search found 2 matches

by James13
Thu Oct 12, 2017 8:07 am
Forum: Real Analysis
Topic: Open subset
Replies: 3
Views: 4058

Re: Open subset

Welcome
by James13
Thu Oct 05, 2017 9:49 pm
Forum: Real Analysis
Topic: Open subset
Replies: 3
Views: 4058

Re: Open subset

Since $G$ is non empty, let $a \in \displaystyle{\mathbb{R}}$ be a real that belongs to $G$. But then, $a-a$ must also belong to $G$, that is, $0 \in G. \\$ Now since $G$ is open, there must exist an open interval around $0$, say $(-\delta,\delta) \subseteq G$ with $\delta >0$. Now pick any positive...