## Check my proof on inequalities please?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Attached Thumbnails

 PhysOrg.com science news on PhysOrg.com >> Galaxies fed by funnels of fuel>> The better to see you with: Scientists build record-setting metamaterial flat lens>> Google eyes emerging markets networks
 First of all, there is a typo in the second step of your solution, you lost your epsilon on the right hand side of the inequality. Second, this is an "if and only if" statement, which means you need to prove the forward direction (Assume |x-a|
 Following your recommendation, the only way I see the forward direction happening, is to write my expression in an opposite order.

## Check my proof on inequalities please?

 Quote by phillyolly Following your recommendation, the only way I see the forward direction happening, is to write my expression in an opposite order.
Right, as I said, in this proof the steps are reversible. In general for "if and only if" proofs though, this is not the case; the forward and backward direction proofs will be different.

EDIT: Check out the proof under "Example: Division" for an illustration of what I mean: http://zimmer.csufresno.edu/~larryc/...andonlyif.html
 Thread Tools

 Similar Threads for: Check my proof on inequalities please? Thread Forum Replies Calculus & Beyond Homework 2 Set Theory, Logic, Probability, Statistics 5 Calculus & Beyond Homework 3 Calculus & Beyond Homework 1 Calculus & Beyond Homework 16