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Topic: A Point on Understanding
Replies: 66   Last Post: Jan 6, 2013 11:07 PM

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 kirby urner Posts: 2,472 Registered: 11/29/05
Re: A Point on Understanding
Posted: Dec 27, 2012 6:24 PM
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On Thu, Dec 27, 2012 at 3:08 PM, Robert Hansen <bob@rsccore.com> wrote:
>
> On Dec 27, 2012, at 6:02 PM, kirby urner <kirby.urner@gmail.com> wrote:
>
> n * (360 - v) = 720
>
>
> Fine, I was trying to help you see more easily, just substitute that into
> what I said...
>
> The limit(n) * limit(360 - v) as n->infinity and v->360 IS NOT THE SAME AS
> limit(n * (360 - v)) as n->infinity and v->360 BECAUSE limit (n) as
> n->infinity DOES NOT EXIST.
>
> Bob Hansen

I don't think your straw man argument helps my students understand how
adding the fact of curvature changes the answer.

The limit (360 - v) really could be 0 if perfect flatness is allowed,
but when we add the constraint of curvature, then even though
everything locally seems to stay the same -- given the epsilon / delta
treatment alone (Debater A) -- the added fact of curvature is new
information and tells us that as n --> infinity, there's a 720
involved (Debater B).

We didn't have that before. Curvature subtracts fractions of a degree
from each vertex. That's knowledge of a global constraint that evades
detection under the microscope.

Kirby

Date Subject Author
12/15/12 Robert Hansen
12/17/12 kirby urner
12/18/12 Robert Hansen
12/17/12 Haim
12/18/12 Robert Hansen
12/26/12 kirby urner
12/26/12 Robert Hansen
12/26/12 kirby urner
12/27/12 Paul A. Tanner III
12/27/12 kirby urner
12/27/12 Robert Hansen
12/27/12 kirby urner
12/27/12 Robert Hansen
12/27/12 kirby urner
12/27/12 Robert Hansen
12/27/12 kirby urner
12/27/12 Robert Hansen
12/27/12 kirby urner
12/28/12 Paul A. Tanner III
12/28/12 kirby urner
12/28/12 Paul A. Tanner III
12/30/12 kirby urner
12/30/12 Louis Talman
12/30/12 kirby urner
12/30/12 kirby urner
12/30/12 kirby urner
12/30/12 Paul A. Tanner III
12/30/12 kirby urner
12/30/12 Paul A. Tanner III
12/27/12 Domenico Rosa
12/27/12 Robert Hansen
12/27/12 Richard Strausz
12/27/12 Domenico Rosa
12/30/12 Joe Niederberger
12/30/12 Paul A. Tanner III
12/30/12 Robert Hansen
12/30/12 Joe Niederberger
12/31/12 Robert Hansen
1/2/13 kirby urner
12/30/12 Joe Niederberger
1/1/13 Paul A. Tanner III
12/31/12 GS Chandy
12/31/12 Robert Hansen
1/1/13 GS Chandy
12/31/12 GS Chandy
12/31/12 Robert Hansen
12/31/12 Joe Niederberger
1/1/13 Robert Hansen
1/1/13 GS Chandy
1/1/13 GS Chandy
1/1/13 GS Chandy
1/1/13 Robert Hansen
1/1/13 Haim
1/1/13 Joe Niederberger
1/1/13 Joe Niederberger
1/1/13 Paul A. Tanner III
1/1/13 Louis Talman
1/2/13 Paul A. Tanner III
1/1/13 Joe Niederberger
1/2/13 Paul A. Tanner III
1/2/13 GS Chandy
1/2/13 Joe Niederberger
1/4/13 Joe Niederberger
1/5/13 GS Chandy
1/5/13 GS Chandy
1/6/13 Robert Hansen
1/6/13 GS Chandy

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