How to use convergence to prove other things

What we need to do:

Very often, the right thing to do is to look for a clever choice of d, and then use convergence to say that you can for sure find an N so that |x_n-a|< d for n beyond N.

In any event, using convergence is exactly the opposite from proving convergence: You don't have to use an arbitrary d, and most of the time, it's important to make a particular, explicit choice of d.

What we say (oftentimes):

Let d=(some appropriate choice)....

...and end up getting what we want

What we want to do:

Example:

Question

Solution

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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: June 13, 1995