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Topic: A question about straight lines
Replies: 103   Last Post: Feb 8, 2014 8:28 AM

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 Joe Niederberger Posts: 2,635 Registered: 10/12/08
Re: A question about straight lines
Posted: Jan 28, 2014 2:11 PM

Neighbor says:
>About the "open ray": how can a finite straight-line have no boundary???? Being made of points, there must be two boundaries in both directions, which we call endpoints, for if there is no boundary this is not a finite straight-line but an infinite one.

You are correct that the "boundary" is the same point for both AG and GB, but that boundary point "G" can be considered either included (the "closed" situation) or excluded ("open") in either AG or GB. Being a boundary and belonging to the set to which it is a boundary are separate notions, and one does not follow logically from the other.

If you want the two segments to overlap at G, then you set theoretically consider it "included" in both AG & GB. (There is no logical conflict in including the number "2" in two distinct sets, say { 1, 2 } and { 1, 2, 3 } - same here.) If you want the two segments to be disjoint, then one or the other or both need to be open. If you want to recover the segment AB by "unioning" the two fragments set theoretically and also keep AG & GB disjoint, then one has to be open and the other closed. This is all elementary set theory applied to line segments considered as sets of point.

Cheers,
Joe N

Date Subject Author
1/26/14 Neighbor
1/26/14 kirby urner
1/27/14 Neighbor
1/27/14 Robert Hansen
1/27/14 Bishop, Wayne
1/27/14 kirby urner
1/27/14 Neighbor
1/27/14 Robert Hansen
1/27/14 Neighbor
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1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
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1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
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1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Robert Hansen
1/28/14 Neighbor
1/28/14 Gary Tupper
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Louis Talman
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
1/29/14 Robert Hansen
1/29/14 Bishop, Wayne
1/29/14 GS Chandy
1/29/14 Domenico Rosa
1/29/14 Neighbor
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1/29/14 Neighbor
1/29/14 Domenico Rosa
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1/29/14 Joe Niederberger
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1/29/14 Robert Hansen
1/30/14 Neighbor
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1/30/14 Louis Talman
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1/31/14 Neighbor
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1/31/14 Joe Niederberger
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1/31/14 GS Chandy
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2/1/14 Joe Niederberger
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