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Topic: The Definition of Points
Replies: 1,424   Last Post: May 5, 2007 9:53 PM

 Messages: [ Previous | Next ]
 briggs@encompasserve.org Posts: 404 Registered: 12/6/04
Re: The Definition of Points
Posted: May 2, 2007 7:16 AM

> briggs@encompasserve.org wrote:
>>> How could anything be "flat out wrong" "without further clarification"?
>>> If they aren't wrong WITH further clarification, then they aren't
>>> "flat-out" wrong. Anyway....
>>>
>>> A "cube" is a form where each element, a point, is connected, though an
>>> edge, to n others out of a total of 2^n, such that any one can connect
>>> indirectly to any other through a series of n such connections or fewer,
>>> and there exists one element for each which requires exactly n such
>>> connections. How's that for a definition of a square of n dimensions? :)

>>
>> Not good. This appears to be a partial characterization rather than
>> a complete definition.
>>
>> I can come up with a three dimensional "cube" that fits
>> this definition but which is not the same as the standard cube.
>>
>> Nodes A through H
>> Edges AB AC AH BC BD CD DE EF EG FG FH GH
>>
>> Graphically
>> B F
>> /|\ /|\
>> --A | D--E | H--
>> \|/ \|/
>> C G
>>
>> 8 nodes
>> Each node with 3 edges
>> All interconnected using no node-to-node paths longer than 3 edges
>> Each node needing at least one 3 edge path to reach at least one other node
>>
>> Note that in a conventional "cube", each node is a "corner" that has
>> exactly one "opposite corner" that is exactly 3 edges away.

>
> See above, where n is the number of dimensions:
>
> "there exists one element for each which requires exactly n such
> connections".

Note that you used "exactly n" but not "exactly one".

This implies that "one" may be read as "at least one". If you
had meant "exactly one" it's clear that you knew how to phrase it.

So your definition is bad because it doesn't say what you intended for
it to say.

Date Subject Author
3/13/07 DontBother@nowhere.net
3/13/07 Ross Finlayson
3/13/07 DontBother@nowhere.net
3/17/07 Anonym1723
3/18/07 DontBother@nowhere.net
3/13/07 PD
3/13/07 SucMucPaProlij
3/13/07 DontBother@nowhere.net
3/19/07 G.E. Ivey
3/19/07 DontBother@nowhere.net
4/17/07 BezekMarcus@aol.com
4/18/07 DontBother@nowhere.net
4/20/07 Michael Press
4/20/07 David R Tribble
3/13/07 Jesse F. Hughes
3/13/07 DontBother@nowhere.net
3/13/07 OG
3/14/07 DontBother@nowhere.net
3/14/07 OG
3/14/07 DontBother@nowhere.net
3/13/07 DontBother@nowhere.net
3/13/07 Sam Wormley
3/13/07 DontBother@nowhere.net
3/14/07 Aaron
3/15/07 DontBother@nowhere.net
3/13/07 Douglas Eagleson
3/13/07 Douglas Eagleson
3/13/07 DontBother@nowhere.net
3/13/07 DontBother@nowhere.net
3/13/07 SucMucPaProlij
3/13/07 Clifford J. Nelson
3/13/07 SucMucPaProlij
3/13/07 Clifford J. Nelson
3/13/07 SucMucPaProlij
3/13/07 Clifford J. Nelson
3/13/07 SucMucPaProlij
3/14/07 DontBother@nowhere.net
4/22/07 John Ryskamp
3/14/07 DontBother@nowhere.net
3/14/07 SucMucPaProlij
3/14/07 Dr. David Kirkby
3/14/07 SucMucPaProlij
3/14/07 Dr. David Kirkby
3/14/07 DontBother@nowhere.net
3/14/07 DontBother@nowhere.net
3/14/07 DontBother@nowhere.net
3/14/07 DontBother@nowhere.net
3/14/07 SucMucPaProlij
3/14/07 DontBother@nowhere.net
3/14/07 Dr. David Kirkby
3/15/07 DontBother@nowhere.net
3/14/07 Sam Wormley
3/15/07 Dr. David Kirkby
3/15/07 Sam Wormley
3/15/07 Dr. David Kirkby
3/15/07 Sam Wormley
3/15/07 Dr. David Kirkby
3/15/07 DontBother@nowhere.net
3/15/07 Eric Gisse
3/15/07 Dr. David Kirkby
3/16/07 Eric Gisse
3/16/07 DontBother@nowhere.net
3/16/07 DontBother@nowhere.net
3/16/07 DontBother@nowhere.net
3/16/07 hagman
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3/15/07 DontBother@nowhere.net
3/16/07 Sam Wormley
3/16/07 DontBother@nowhere.net
3/15/07 DontBother@nowhere.net
3/15/07 DontBother@nowhere.net
3/16/07 Sam Wormley
3/16/07 DontBother@nowhere.net
3/16/07 Sam Wormley
3/17/07 DontBother@nowhere.net
3/17/07 Sam Wormley
3/18/07 DontBother@nowhere.net
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3/16/07 Sam Wormley
3/16/07 DontBother@nowhere.net
3/16/07 Sam Wormley
3/17/07 DontBother@nowhere.net
3/17/07 Sam Wormley
3/18/07 DontBother@nowhere.net
3/15/07 SucMucPaProlij
3/15/07 DontBother@nowhere.net
3/16/07 Brian Chandler
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3/16/07 bjacoby@iwaynet.net
3/16/07 mmeron@cars3.uchicago.edu
3/16/07 DontBother@nowhere.net
3/16/07 Virgil
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3/16/07 Wolf
3/16/07 DontBother@nowhere.net
3/16/07 DontBother@nowhere.net
3/13/07 DontBother@nowhere.net
3/13/07 SucMucPaProlij
3/14/07 DontBother@nowhere.net
3/14/07 The_Man
3/14/07 DontBother@nowhere.net
3/14/07 Sam Wormley
3/15/07 DontBother@nowhere.net
3/16/07 Sam Wormley
3/16/07 DontBother@nowhere.net
3/16/07 Sam Wormley
3/17/07 DontBother@nowhere.net
3/17/07 Sam Wormley
3/18/07 DontBother@nowhere.net
3/14/07 VK
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3/14/07 PD
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3/15/07 Dr. David Kirkby
3/15/07 DontBother@nowhere.net
3/15/07 PD
3/16/07 DontBother@nowhere.net
3/18/07 PD
3/18/07 DontBother@nowhere.net
3/18/07 PD
3/19/07 Tony Orlow
3/19/07 PD
3/19/07 Tony Orlow
3/20/07 DontBother@nowhere.net
3/20/07 Dr. David Kirkby
3/20/07 DontBother@nowhere.net
3/21/07 Tony Orlow
3/21/07 DontBother@nowhere.net
3/21/07 Tony Orlow
3/22/07 DontBother@nowhere.net
3/22/07 Tony Orlow
3/22/07 DontBother@nowhere.net
3/20/07 stephen@nomail.com
3/21/07 Tony Orlow
3/21/07 Mike Kelly
3/21/07 Tony Orlow
3/21/07 Mike Kelly
3/21/07 Tony Orlow
3/21/07 Mike Kelly
3/21/07 Tony Orlow
3/22/07 Mike Kelly
3/22/07 DontBother@nowhere.net
3/21/07 Virgil
3/21/07 Tony Orlow
3/22/07 Virgil
3/22/07 DontBother@nowhere.net
3/22/07 DontBother@nowhere.net
3/21/07 DontBother@nowhere.net
3/21/07 Tony Orlow
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3/22/07 DontBother@nowhere.net
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3/22/07 Tony Orlow
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3/23/07 Randy Poe
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3/22/07 DontBother@nowhere.net
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3/22/07 Tony Orlow
3/23/07 DontBother@nowhere.net
3/23/07 PD
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3/24/07 PD
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3/22/07 Tony Orlow
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3/24/07 Tony Orlow
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3/29/07 Tony Orlow
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4/18/07 Jack Markan
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4/13/07 Chas Brown
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5/2/07 briggs@encompasserve.org
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4/19/07 Jack Markan
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3/31/07 DontBother@nowhere.net
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3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
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4/13/07 DontBother@nowhere.net
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3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
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4/12/07 DontBother@nowhere.net
4/13/07 Tony Orlow
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4/13/07 Tony Orlow
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4/17/07 Tony Orlow
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3/29/07 DontBother@nowhere.net
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3/30/07 Tony Orlow
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3/31/07 Dr. David Kirkby
4/1/07 DontBother@nowhere.net
3/31/07 Tony Orlow
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4/1/07 DontBother@nowhere.net
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3/30/07 Tony Orlow
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3/31/07 Mike Kelly
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3/31/07 Virgil
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4/1/07 Virgil
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4/1/07 Mike Kelly
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4/12/07 Tony Orlow
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4/12/07 Jack Markan
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3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
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3/29/07 nonsense@unsettled.com
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3/30/07 Tony Orlow
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3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
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3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
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3/30/07 Tony Orlow
3/30/07 Virgil
3/30/07 stephen@nomail.com
3/31/07 Tony Orlow
3/31/07 Brian Chandler
3/31/07 Tony Orlow
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4/18/07 Tony Orlow
4/18/07 Jack Markan
4/18/07 Mike Kelly
4/18/07 Virgil
4/19/07 Tony Orlow
4/19/07 Jack Markan
4/19/07 Brian Chandler
4/17/07 stephen@nomail.com
4/17/07 DontBother@nowhere.net
4/18/07 Tony Orlow
4/18/07 stephen@nomail.com
4/18/07 DontBother@nowhere.net
4/19/07 Tony Orlow
4/19/07 stephen@nomail.com
4/19/07 David R Tribble
4/19/07 DontBother@nowhere.net
4/20/07 David R Tribble
4/20/07 Tony Orlow
4/20/07 Virgil
4/21/07 stephen@nomail.com
4/23/07 Tony Orlow
4/23/07 Virgil
4/23/07 Tony Orlow
4/23/07 Virgil
4/14/07 DontBother@nowhere.net
4/14/07 Mike Kelly
4/14/07 Tony Orlow
4/14/07 Virgil
4/17/07 Tony Orlow
4/17/07 Virgil
4/18/07 Tony Orlow
4/18/07 Virgil
4/17/07 Mike Kelly
4/14/07 DontBother@nowhere.net
4/14/07 DontBother@nowhere.net
4/2/07 Virgil
4/12/07 Tony Orlow
4/12/07 K_h
4/1/07 Dr. David Kirkby
4/1/07 Mike Kelly
4/1/07 Dr. David Kirkby
3/31/07 DontBother@nowhere.net
3/31/07 stephen@nomail.com
3/31/07 Tony Orlow
3/31/07 stephen@nomail.com
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
4/1/07 Virgil
3/31/07 stephen@nomail.com
3/31/07 Tony Orlow
3/31/07 stephen@nomail.com
3/31/07 Tony Orlow
3/31/07 Chas Brown
4/1/07 Tony Orlow
4/1/07 Mike Kelly
4/1/07 Chas Brown
4/1/07 stephen@nomail.com
4/1/07 Virgil
4/2/07 DontBother@nowhere.net
4/1/07 stephen@nomail.com
3/31/07 Virgil
3/31/07 Brian Chandler
3/31/07 stephen@nomail.com
3/31/07 Tony Orlow
3/31/07 Mike Kelly
3/31/07 Tony Orlow
4/1/07 Mike Kelly
4/1/07 DontBother@nowhere.net
3/31/07 stephen@nomail.com
3/31/07 Tony Orlow
4/1/07 stephen@nomail.com
4/1/07 Brian Chandler
4/1/07 DontBother@nowhere.net
4/1/07 DontBother@nowhere.net
4/1/07 Chas Brown
4/1/07 DontBother@nowhere.net
4/1/07 DontBother@nowhere.net
3/31/07 Virgil
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Chas Brown
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Chas Brown
3/31/07 Tony Orlow
3/31/07 Chas Brown
4/1/07 Virgil
4/1/07 Tony Orlow
4/1/07 Virgil
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 DontBother@nowhere.net
3/30/07 Mike Kelly
3/31/07 Brian Chandler
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
3/31/07 Tony Orlow
3/31/07 Mike Kelly
3/31/07 Tony Orlow
3/31/07 Brian Chandler
3/31/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Mike Kelly
3/31/07 Tony Orlow
3/31/07 Chas Brown
3/31/07 Tony Orlow
4/1/07 Chas Brown
4/1/07 Tony Orlow
4/1/07 Virgil
4/2/07 DontBother@nowhere.net
4/1/07 Virgil
4/1/07 Mike Kelly
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/30/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
3/31/07 Tony Orlow
3/31/07 Virgil
4/2/07 Jack Markan
4/12/07 Tony Orlow
4/12/07 Jack Markan
4/12/07 DontBother@nowhere.net
4/12/07 Jack Markan
4/13/07 DontBother@nowhere.net
4/13/07 Tony Orlow
4/13/07 Jack Markan
4/13/07 Virgil
4/13/07 DontBother@nowhere.net
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
3/29/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
4/12/07 Tony Orlow
4/12/07 DontBother@nowhere.net
4/13/07 Tony Orlow
4/13/07 DontBother@nowhere.net
4/17/07 Tony Orlow
4/17/07 DontBother@nowhere.net
4/18/07 Tony Orlow
4/18/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
4/12/07 Tony Orlow
4/13/07 DontBother@nowhere.net
4/13/07 Tony Orlow
4/13/07 DontBother@nowhere.net
4/17/07 Tony Orlow
4/17/07 DontBother@nowhere.net
4/18/07 Tony Orlow
4/19/07 DontBother@nowhere.net
4/19/07 David R Tribble
4/19/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
3/29/07 DontBother@nowhere.net
3/30/07 Tony Orlow
3/31/07 DontBother@nowhere.net
3/31/07 Tony Orlow
4/1/07 DontBother@nowhere.net
4/12/07 Tony Orlow
4/13/07 DontBother@nowhere.net
4/13/07 Tony Orlow
4/14/07 DontBother@nowhere.net
4/17/07 Tony Orlow
4/17/07 DontBother@nowhere.net
4/17/07 DontBother@nowhere.net
4/17/07 DontBother@nowhere.net
4/17/07 DontBother@nowhere.net
4/17/07 DontBother@nowhere.net
4/17/07 DontBother@nowhere.net
4/18/07 Tony Orlow
4/19/07 DontBother@nowhere.net
4/20/07 Tony Orlow
4/21/07 DontBother@nowhere.net
4/23/07 Tony Orlow
4/23/07 DontBother@nowhere.net
4/23/07 Ben newsam
4/23/07 Dr. David Kirkby
4/24/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/23/07 Tony Orlow
4/24/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/24/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/24/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/25/07 DontBother@nowhere.net
4/25/07 Ben newsam
4/26/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/24/07 Ben newsam
4/25/07 DontBother@nowhere.net
4/25/07 DontBother@nowhere.net
4/25/07 Ben newsam
4/26/07 DontBother@nowhere.net
4/26/07 Tony Orlow
4/26/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/25/07 DontBother@nowhere.net
4/26/07 Tony Orlow
4/26/07 DontBother@nowhere.net
4/24/07 DontBother@nowhere.net
4/24/07 Tony Orlow
4/25/07 DontBother@nowhere.net
4/26/07