Search found 3 matches
- Fri Oct 14, 2016 3:19 am
- Forum: Real Analysis
- Topic: Real Analysis
- Replies: 1
- Views: 2655
Real Analysis
Let $S=[0,1]$. If $x$ and $y$ are in $S$ with $x\neq y$. How can we show that there are $m,n\in \mathbb{N}$ such that $x< \dfrac{m}{2^n} <y$. Can the Archimedean Property be used to prove this? If yes, could anyone provide me an insight to do this?
- Fri Oct 14, 2016 2:47 am
- Forum: Real Analysis
- Topic: Real Analysis
- Replies: 0
- Views: 1919
Real Analysis
Let's call a set "Pseudo compact" if it has the property that every closed cover (a cover consisting of closed sets) have a finite subcover. I have a little ides on "Anti-Compact: subsets. Does Pseudo-Compact in this case the same as Anti-Compact ? Then how can we describe the "P...
- Fri Oct 14, 2016 2:34 am
- Forum: Real Analysis
- Topic: Real Analysis
- Replies: 1
- Views: 2479
Real Analysis
I am aware a set is Bounded if it has both upper and Lower bounds and i know what a Limit point of a set is but i am finding it hard to show that If $S\subset\mathbb{R}$ be a "bounded infinite set", then $S'\neq\varnothing$ .