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

Prove that lim x→1 of x^{2}does not equal 1+10^{-10}. You could use a proof by contradiction.

(It is question 2.b here)

2. Relevant equations

δ-ε proofs!

3. The attempt at a solution

Given ε > 0, there is some number δ > 0 such that if:

|x - a | < δ

|x - 0 | < δ

|x| < δ

Then:

| f(x) - L | < ε

| x^{2}- 1+10^{-10}| < ε

...and here's where I get stuck. Delta-epsilon proofs always seemed a bit circular to me, and what confuses me about proving "by contradiction" here is the fact that I should be able to choose some δ and the limit WOULD approach 1+10^{-10}:s... I'm a bit lost on where to go from here!

**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: How to do a delta-epsilon proof by contradiction?

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