(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the real numbers a and b are equal if and only if for each positive real e, the absolute value of a-b satisfies abs(a-b)<e

2. Relevant equations

The main one I am thinking about is the fact that if a<=b and b<=a then a=b, also the whole sigma thing might mean the archimedean property might come into effect (if r and s are positive ration numbers then there exists a positive integer N such that rN<s).

3. The attempt at a solution

I am tried a proof by contradiction.... but generally it falls apart or requires too much non-rigorous work :-/

Any ideas/hints/help?

Thanks!

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

Dismiss Notice

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: Analysis Equality

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