Epsilon-Delta Proofs: Understanding the Process

[David_Vancouver]

Hi,

Why is it, that when ever epsilon-delta proofs are done, once delta is found in terms of epsilon, it is reinputed through again? Is there any point to this really?

 

[Euclid]

The idea is that you make some suggestive calculations to help you find what delta should be. Then you have to go back and make sure it actually works. If you were clever, you could guess delta and then show it works, and skip the finding delta part.

 

[David_Vancouver]

But aren't those suggestive calculations definitive? That is, they are always true?

 

[shmoe]

It's not necessary to reorganize your proof in a way that makes the delta magically appear from thin air, but it often makes a shorter proof. It's mostly for style reasons.