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Techniques of Proof

Introduction

Writing your own proofs is the part of analysis that gets sold to you as hard problem solving, and that's certainly true. But there's also, very definitely, an aspect to writing proofs which is much more routine. Good workmanship, you might call it.

For numerous types of problems there are standard approaches to try, or standard ways of setting up the problem. If you're confident in the right way to set the problem up, then you're that much more likely to be able to reduce a problem you can't solve to one which you can. At any rate, you should be able to pare away the layers of notation and definition, and get to the key idea. (Most of the problems you come across in this course really just have one key idea, but that can be hidden by the phrasing.

The point of this page is to bring together a number of types of problem, and discuss how you'd set them to solve them. I'm going to add topics on types of problem as I think of them.

Please request more topics, whenever you think of one!! That's how the page will grow.

Types of Problem

Showing two sets are equal

Showing a set is open

Showing a set is closed

How to show a sequence converges

How to use a convergent sequence (to prove other things)

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1995 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: Novemebr 18, 1995