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Topic: Visual Presentation of Real Number System
Replies: 61   Last Post: Dec 11, 2013 11:12 PM

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Joe Niederberger

Posts: 3,081
Registered: 10/12/08
Re: Visual Presentation of Real Number System
Posted: Nov 25, 2013 2:51 PM
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R Hansen says:
>And, if we take that the smallest actual "point" on a drawn line would be represented by the centers of the molecules or atoms of the ink/lead, then I would suspect that those locations are all at irrational distances from the end (transcendental in fact).

Really? You think physical distances are truly all irrational? And then what distance could ever be demarcated as 1?

R Hansen says:
>I think the hardest aspect of the irrationals and rationals to portray in a tangible way is that between any two rationals there are an infinite number of rationals and an infinite number of "holes".

What I see with my mind's eye is not holes but rather that the minds concept of mathematical "line" and "point" and the relationship between them is just not similar to pebbles laid in a row. And yet a lot of common talk in mathematics is always leaning on that conception. As if the line is made of of a bunch of points (or points and holes).

In my mind at least line and point are distinct species with a curious but easily visualized game that can be played - I can always zoom in to the space between any two points on a line, and find a line segment between them. That line segment is similar in certain respects to any other segment, and so I can play the game over and over. The only thing "tangible" is this notion of a never ending process.

Its also quite "tangible" (in the imaginary sense of "tangible! What??) to view incommensurable lengths in a similar way: imagine (or image ;-) multiple copies of two segments of two incommensurable lengths being laid end to end -- and the frustration that they never, ever line up on the cracks.

Cheers,
Joe N


Date Subject Author
11/21/13
Read Visual Presentation of Real Number System
Jerry P. Becker
11/21/13
Read Re: Visual Presentation of Real Number System
Dave L. Renfro
11/21/13
Read Re: Visual Presentation of Real Number System
Gary Tupper
11/25/13
Read Fwd: Re: Visual Presentation of Real Number System
Gary Tupper
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/25/13
Read Re: Visual Presentation of Real Number System
Gary Tupper
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/25/13
Read Re: Fwd: Re: Visual Presentation of Real Number System
Joe Niederberger
11/21/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/24/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/25/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/25/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/25/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/25/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Louis Talman
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Gary Tupper
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/26/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/27/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/27/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/27/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/27/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/27/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/27/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/27/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/28/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/27/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/28/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/28/13
Read Re: Visual Presentation of Real Number System
GS Chandy
11/28/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/29/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/28/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/29/13
Read Re: Visual Presentation of Real Number System
GS Chandy
11/29/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/29/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
11/29/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
11/29/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
12/4/13
Read Re: Visual Presentation of Real Number System
GS Chandy
12/4/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
12/11/13
Read Re: Visual Presentation of Real Number System
Joe Niederberger
12/11/13
Read Re: Visual Presentation of Real Number System
Robert Hansen
12/11/13
Read Re: Visual Presentation of Real Number System
GS Chandy

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