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

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 Neighbor Posts: 57 From: It doesn't matter Registered: 1/26/14
Re: A question about straight lines
Posted: Jan 28, 2014 5:36 PM

> "Two consecutive points" has no meaning in the real
> number based
> continuum, or even in the set of rational numbers
> with usual ordering. So, if you cannot accept that
> between two real (or rational) numbers there is
> always another (which means that "two consecutive"
> simply does not exist in these games) then you will
> never accept the more or less accepted answers to

You are mentioning a straight-line with numbers on it, and since you can always find a number between two others, being this number on the straight-line, between two numbers on the straight-line there will be another, but I want you to explain me the nature of a straight-line in Euclid's geometry, not putting numbers on the straight-line, and not saying that what for numbers is true is also true for straight-lines. 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.

> So, lets simplify a bit: can you accept that between
> two points their is always another? Why or why not?
> If you do accept that, then what possible meaning
> does "two consecutive points" have? Any two you pick,
> trying to get that elusive consecutive pair, will
> always have another between them. Therefore they are
> not consecutive.
>
> Cheers,
> Joe N

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. Therefore, unless you show me how we can solve the aforementioned problem with the admission that between two points there is another, I cannot help thinking that two consecutive points exist.

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
1/27/14 Neighbor
1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Robert Hansen
1/28/14 Neighbor
1/28/14 Robert Hansen
1/28/14 Joe Niederberger
1/28/14 Joe Niederberger
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
1/29/14 Joe Niederberger
1/29/14 Neighbor
1/29/14 Domenico Rosa
1/30/14 Bishop, Wayne
1/29/14 Joe Niederberger
1/29/14 Neighbor
1/29/14 Robert Hansen
1/29/14 Joe Niederberger
1/29/14 Joe Niederberger
1/29/14 Robert Hansen
1/30/14 Neighbor
1/29/14 Robert Hansen
1/29/14 Joe Niederberger
1/30/14 Louis Talman
1/29/14 Joe Niederberger
1/30/14 Neighbor
1/30/14 Jonathan J. Crabtree
1/30/14 Joe Niederberger
1/30/14 Joe Niederberger
1/31/14 kirby urner
1/30/14 Joe Niederberger
1/31/14 Neighbor
1/30/14 Joe Niederberger
1/31/14 Neighbor
1/31/14 Robert Hansen
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Robert Hansen
1/31/14 Joe Niederberger
1/31/14 Neighbor
1/31/14 Robert Hansen
1/31/14 Joe Niederberger
1/31/14 Joe Niederberger
1/31/14 Robert Hansen
1/31/14 Neighbor
1/31/14 Robert Hansen
1/31/14 GS Chandy
1/31/14 GS Chandy
1/31/14 GS Chandy
1/31/14 Joe Niederberger
2/1/14 GS Chandy
2/1/14 Robert Hansen
2/1/14 kirby urner
2/1/14 Robert Hansen
2/1/14 Joe Niederberger
2/1/14 Robert Hansen
2/1/14 Joe Niederberger
2/2/14 Robert Hansen
2/2/14 kirby urner
2/1/14 Joe Niederberger
2/2/14 Robert Hansen
2/2/14 James Elander
2/2/14 GS Chandy
2/2/14 Robert Hansen
2/2/14 GS Chandy
2/2/14 Robert Hansen
2/2/14 Joe Niederberger
2/2/14 GS Chandy
2/2/14 Robert Hansen
2/2/14 GS Chandy
2/4/14 GS Chandy
2/4/14 GS Chandy
2/4/14 GS Chandy
2/8/14 GS Chandy