Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Education » math-teach

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robert Hansen

Posts: 7,715
From: Florida
Registered: 6/22/09
Re: Visual Presentation of Real Number System
Posted: Nov 29, 2013 1:56 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
att1.html (7.4 K)


On Nov 28, 2013, at 9:19 PM, Joe Niederberger <niederberger@comcast.net> wrote:

> Happening, selecting, picking are either physics, or computation. To paraphrase Yoda, "The real number
> just is, there is no picking".
>
>
> My problem is not with infinite digits. You cannot actually pick a random real (or at least ever finish picking it.)


I don't know why you are having a problem with this. You make it sound like Zeno's paradoxes are actual paradoxes. And it isn't infinite digits, it is an infinite *sequence* of digits. You are right, we never finish picking it, like we never finish 1/2 + 1/4 + 1/8 + 1/(2^n)..., but we know the sum is 1. You started with the reasonable argument that a ray of light would never hit a particular number. All I did is realize that the ray of light must hit a non particular number, which we know realize is an uncomputable number.


> This business of saying "it happens all the time" is pure H.S. That is neither logical, or mathematical. For an example that is easier to unwind, look up the formal definition of the axiom of choice. There is no choosing involved.

I didn't see this discussion as being so odd that we needed to unwind it.

>
>
> The metaphors of choosing, or "picking a random real" are crutches, much like those pictures you are always railing against. I think those metaphors though, are more insidious than pictures, because while its easy for a mathematically mature person to distinguish between a picture and the mathematics that may map to that picture, the metaphors surrounding probability are more ingrained and unconscious.


Using physics metaphorically is not a problem, when, as you stated, it is done by a mathematically mature person. Even using pictures is not a problem under the same circumstances. When I draw a line and say it is a mathematical line I am speaking metaphorically. Actual physics gets around this because it uses constants which are uncomputable numbers. The speed of light is an uncomputable number. Plank's constant is an uncomputable number. In every sense of this discussion.

I still am not sure what your issue is. You started with the argument of the impossibility of a ray of light hitting a particular number, which I found reasonable. I just realized, along the same line of reasoning, the ray of light couldn't hit any particular number. It seems that it hits an uncomputable number. Do you have a problem with the idea of an uncomputable number? Or is it with my infinite sequence argument concluding with the comparison of the size of the set of uncomputable numbers and computable numbers?

Bob Hansen



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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.