I'm having a little difficulty understanding Epsilon in the definition of convergence. From what the book says it is any small real number greater than zero (as small as you can imagine???). Also, since I don't quite grasp what this epsilon is and how it helps define convergence, I am having difficulty applying it to the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

Let b=Least upper bound of a set S (S is a subset of the real numbers) that is bounded and non empty. Then Given epsilon greater than 0, there exists an s in S such that (b-Epsilon)<= s <= b.

I started by proving that there exists an s in S, but I cannot figure out how to relate this all to epsilon.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Real Analysis- least upper bound and convergence

**Physics Forums | Science Articles, Homework Help, Discussion**