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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: 2,861
Registered: 10/12/08
Re: A question about straight lines
Posted: Jan 28, 2014 6:08 PM
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Neighbor says:
>Just now I want to deal only with straight-lines and points on them, as Euclid does in the Elements, without putting numbers on them.

Euclid didn't deal with point set topology as far as I know - that's more or less where your questions are leading. I suppose Euclid would say one could divide a line segment into two equal length parts, but he didn't look real closely at the endpoints, or much care about the so-called individual points in that sense. In today's viewpoint, you can divide a line segment (separate into two disjoint sets) into two segments with lengths of equal measure, but that doesn't mean they are topologically exactly the same when you care about such fine matters as the endpoints. Having one segment with a closed endpoint doesn't make it "longer" than the other, open ended segment so Euclid was right, if a bit course grained.

Neighbor says:
>If I accept that between two points there is always another, then there is the aforementioned problem of division of a straight-line in half, which I cannot understand if I admit that between two points there's always another.

What problem?

See my other answer about what's bothering you. You seem to think one "should" be able to "symmetrically" divide a line segment in two (topologically) equivalent parts or something like that. Why *should* one be able to do that? Why *should* one be able to trisect and angle with straight-edge and compass? Why *should* any number of mathematical absurdities actually exist?

Cheers,
Joe N


Date Subject Author
1/26/14
Read A question about straight lines
Neighbor
1/26/14
Read Re: A question about straight lines
kirby urner
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Robert Hansen
1/27/14
Read Re: A question about straight lines
Bishop, Wayne
1/27/14
Read Re: A question about straight lines
kirby urner
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Robert Hansen
1/27/14
Read Re: A question about straight lines
Neighbor
1/27/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Neighbor
1/28/14
Read Re: A question about straight lines
Gary Tupper
1/28/14
Read Re: A question about straight lines
Robert Hansen
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Louis Talman
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/28/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Bishop, Wayne
1/29/14
Read Re: A question about straight lines
GS Chandy
1/29/14
Read Re: A question about straight lines
Domenico Rosa
1/29/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Domenico Rosa
1/30/14
Read Re: A question about straight lines
Bishop, Wayne
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/30/14
Read Re: A question about straight lines
Neighbor
1/29/14
Read Re: A question about straight lines
Robert Hansen
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Louis Talman
1/29/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Neighbor
1/30/14
Read Re: A question about straight lines
Jonathan Crabtree
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
kirby urner
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/30/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Joe Niederberger
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
Neighbor
1/31/14
Read Re: A question about straight lines
Robert Hansen
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
GS Chandy
1/31/14
Read Re: A question about straight lines
Joe Niederberger
2/1/14
Read Re: A question about straight lines
GS Chandy
2/1/14
Read Re: A question about straight lines
Robert Hansen
2/1/14
Read Re: A question about straight lines
kirby urner
2/1/14
Read Re: A question about straight lines
Robert Hansen
2/1/14
Read Re: A question about straight lines
Joe Niederberger
2/1/14
Read Re: A question about straight lines
Robert Hansen
2/1/14
Read Re: A question about straight lines
Joe Niederberger
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
kirby urner
2/1/14
Read Re: A question about straight lines
Joe Niederberger
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
James Elander
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
Joe Niederberger
2/2/14
Read Re: A question about straight lines
GS Chandy
2/2/14
Read Re: A question about straight lines
Robert Hansen
2/2/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/4/14
Read Re: A question about straight lines
GS Chandy
2/8/14
Read Re: A question about straight lines
GS Chandy

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