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## #1 Help Me ! » Supremum Property of Real Number » 2016-10-13 14:44:09

Sheff
Replies: 1

Let S = [0,1]. If x and y are in s with x ≠y. How can we show that there are m,n∈N such that x< m/2^n <y. Can the Archimedean Property be used to prove this? If yes, could anyone provide me an insight to do this?

## #2 Help Me ! » Limit Points of a Set » 2016-10-13 14:42:44

Sheff
Replies: 2

I am aware a set is Bounded if it has both upper and Lower bound and i know what a Limit point of a set is but how can i show that If S ⊂ R be a "bounded infinite set", then S' ≠∅

## #3 Exercises » Real Analysis » 2016-10-13 14:40:22

Sheff
Replies: 0

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.

Does "Pseudo Compact" in this case the same as "Anti-Compact" ? Then how can we describe the "Pseudo-Compact" subsets of Real Numbers?

## #4 Help Me ! » Mathematics Real Analysis » 2016-09-27 21:14:06

Sheff
Replies: 1

Guys i need your help on this. I really do not know whether the solution for a bounded set works well with this as i have the solution to a bounded set.

Find, with proof, a subset of a real number that has only three limit points.

Thanks