Another question: Prove that if a set E in R has a finite infimum and e > 0 is any positive number, then there is a point a in E such that inf E <= a < inf E + e.(adsbygoogle = window.adsbygoogle || []).push({});

The first part, inf E <= a, is obvious from the definition of infimum.

I am having trouble showing that a < inf E + e, even though it seems obvious. My thought is to break it into two cases.

Case 1: inf E = a. Then, we know that since e is strictly greater than 0, that inf E < inf E + e. Thus a < inf E + e.

Case 2: inf E < a. Then what can I use to help me show that a < inf E + e?

Colleen

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

Join Physics Forums Today!

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

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

# Homework Help: Test Review 2 - a property of the infimum

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