is the metric space with metric . Prove:

, for all , where

Not sure what's going on here so I started going backwards for the hell of it:

Is this correct or useful in any way? Can somebody explain this geometrically?

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- October 21st 2010, 07:58 AM #1

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- October 21st 2010, 08:53 AM #2

- October 21st 2010, 09:37 AM #3

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- October 21st 2010, 09:47 AM #4

- October 21st 2010, 10:00 AM #5

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- October 21st 2010, 10:05 AM #6

- October 21st 2010, 10:23 AM #7

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- October 21st 2010, 11:38 AM #8
Well that does clear away the clutter.

Any complex number can be written as where .

The points are on the unit circle for any .

The line determined by intersects the unit circle at .

So the real numbers represent the distances of points on the unit circle at minimum and maximum from .

- October 22nd 2010, 04:14 AM #9

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- October 26th 2010, 08:28 AM #10

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- October 26th 2010, 09:11 AM #11