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Topic: Sequence convergence and absorption
Replies: 12   Last Post: Dec 4, 2009 10:24 AM

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Joel Feinstein

Posts: 32
From: The University of Nottingham
Registered: 2/27/09
Sequence convergence and absorption
Posted: Nov 17, 2009 3:06 PM
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In order to (hopefully!) help my students to understand convergence of sequences better, I have introduced the notion of "absorption": a set absorbs a sequence if, from some term on, all terms of the sequence are within the set. This alternative to the more standard terms "eventually in" and "only finitely many terms outside" has the advantage that it makes the set the subject of the sentence. Consider the following formulation of convergence: a sequence converges to the point a if and only if every open ball centred on a absorbs the sequence.

For some discussion of the possible gains, see the post on my blog.

Today I ran a workshop for my second-year mathematical analysis students on this material. This screencast is available at

Any comments or suggestions would be very welcome!

Best wishes,
Joel Feinstein
Joel Feinstein

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