Re: Critique on Def. of Convergence

On May 9, 1:50 am, fjbl...@xxxxxxxxx wrote:
On May 8, 6:59 pm, Rodo <mattr...@xxxxxxxxx> wrote:

Hi all,

I've been asked to "use the definition of convergence of a sequence to
prove that [my] sequence converges". This is a take-home final
project for one of my classes. I have uploaded what I think is a
clear proof, but I'm sure there's room for a little critique to make
it "straight from the book" as Erdos would say...actually it's
probably no where near that perfect, but I would appreciate any
feeback as to what I can add or change to make it better. You can see
them at:
<br>http://members.aol.com/quikslver182/hompro1.jpg
<br>and<br>http://members.aol.com/quikslver182/hompro2.jpg

Thanks in advance for any suggestions!

It looks pretty good to me. It could probably be simplified some by
using some facts about continuity of various functions, but since you
apparently want to do it from first principles I think it's fine.
However on the first page where you have "since n > N implies |s_n-s|
<e": I don't think you mean "since" because this is what you are
trying to show. In fact I think that clause is really just redundant
and should be omitted.

I must say that the typesetting is pretty ugly. This is probably your
software's fault rather than yours. If you'd like to make a really
nice looking writeup, which will impress your professor and also be
surprisingly satisfying, you might download a copy of LyX (http://www.lyx.org/download/). This is a document processor based on LaTeX,
which is the standard typesetting tool among professional
mathematicians. You could also use LaTeX itself, but LyX is quicker
to learn and the results are almost as nice. Leaning LyX or LaTeX is
a skill which will be very useful as you proceed in mathematics, and
your papers won't hurt the professor's eyes as much.

Hey Nate, thanks so much for your advice! I decided to omit the line
your recommended since your are correct about that is what I'm trying
to show. I also agree that the typesetting is ugly, so thanks for
introducing me to a new program that I look forward to getting to
know. Have a good day.

.

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