
Re: A Point on Understanding
Posted:
Dec 27, 2012 6:24 PM


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

