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February 10th, 2014, 11:29 PM   #1
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Line segment

If (line segments) in a metric geometry, prove that and

How can I prove this?
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February 11th, 2014, 01:41 PM   #2
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Re: Line segment

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Originally Posted by tom33
If (line segments) in a metric geometry, prove that and

How can I prove this?
You need to clarify your notation. Is it possible that A=D and B=C?
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February 11th, 2014, 02:45 PM   #3
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Re: Line segment

Well, the book didn't elaborate on that. I assume since it didn't elaborate then A=D and B=C is not applicable.
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February 12th, 2014, 04:51 PM   #4
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Re: Line segment

How is line segment defined in the book?
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February 13th, 2014, 05:45 AM   #5
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Re: Line segment

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Originally Posted by tom33
Well, the book didn't elaborate on that. I assume since it didn't elaborate then A=D and B=C is not applicable.
Whether it was "elaborated" or not, to do a problem like this you will have to know the definition of a line segment and what it means for two line segments to be equal.
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February 13th, 2014, 06:26 PM   #6
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Re: Line segment

The definition I have, in the book, for line segment is:

If A and B are distinct points in a metric geometry then the line segment from A to B is the set

Where P is the set of points and A-C-B means that the point C is between A and B.
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February 15th, 2014, 01:19 AM   #7
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Re: Line segment

Do you have any idea on how I can prove this?
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February 15th, 2014, 01:44 AM   #8
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What exactly does mean, i.e., what does "between A and B" mean?
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February 16th, 2014, 03:46 PM   #9
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Re: Line segment

C is between A and B if the distance
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