Epsilon-Delta Proofs: Understanding the Process

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Homework Help Overview

The discussion revolves around the process of epsilon-delta proofs in calculus, focusing on the reasoning behind re-evaluating delta after it has been expressed in terms of epsilon.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the rationale behind re-inputting delta after its initial calculation, questioning whether the suggestive calculations are definitive or merely stylistic choices.

Discussion Status

The conversation is ongoing, with participants sharing insights about the necessity and implications of the calculations involved in epsilon-delta proofs. Some guidance is offered regarding the potential for a more efficient proof structure, but no consensus has been reached.

Contextual Notes

Participants are considering the balance between mathematical rigor and stylistic preferences in proof construction, as well as the implications of assumptions made during the proof process.

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

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