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Re: Gray's Differential Geometry error?

• To: mathgroup at smc.vnet.net
• Subject: [mg63199] Re: Gray's Differential Geometry error?
• From: rip pelletier <bitbucket at comcast.net>
• Date: Sun, 18 Dec 2005 07:34:36 -0500 (EST)
• References: <dnv48c$och$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <dnv48c$och$1 at smc.vnet.net>,
 "Steven T. Hatton" <hattons at globalsymmetry.com> wrote:

> 
> It appears to me that, according to his definitions, all the summations on
> page 9 should be from 1 to n, and not 1 to N.  That doesn't matter so much. 
> I can be pretty confident of the intent from the context.  My real
> confusion comes from the epsilon inequality involving N on page 10.  I'm
> not sure which N he means.  Is it the N representing the number of
> partitions of the curve, or is it the N representing the number of
> dimensions in R^n?

it appears to me that you are correct: the summations on p. 9 are to n 
not N. this implies that the N in the delta-epsilon bound on p. 10 is 
supposed to be n also, not N. he applies that common bound on p. 10 to 
each of n terms in the sum that defines Bj.

hope this helps.

oh, i'd call it a wonderful little book; the only problem is that it 
isn't little, of course.

vale,
   rip

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