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

 Messages: [ Previous | Next ]
 Gary Tupper Posts: 544 Registered: 12/3/04
Re: Visual Presentation of Real Number System
Posted: Nov 25, 2013 6:07 PM
 att1.html (3.3 K)

On 11/25/2013 1:59 PM, Robert Hansen wrote:
>
> On Nov 25, 2013, at 4:47 PM, Gary Tupper <gtupper@peda.com
> <mailto:gtupper@peda.com>> wrote:
>

>> So - what would we make of a line that that blinked red & blue, with
>> a single pixel blinking green?

>
> After my epileptic fit or during?:)
>
> I don't understand what you are suggesting by color. That sounds more
> like a symbol than a model. For example, the open circle denoting a
> missing point is a notational device or symbol. A model of a missing
> point would a very tiny gap in the line, but that would be a poor
> model and wouldn't work at the end of the line, thus the use of
>
> Bob Hansen
>

Hi, Bob:

Actually, the gap would be smaller than 'tiny' since its width would be
zero. We should remember that any physical representation of a
mathematical object is a model. The objective of our model is
essentially to impart information - the open circle on a curve is
interpreted to mean that a single point is missing.

Take, for example, the graph of y=x^2 /(x-1) :
Usually drawn as a parabola with a hollow dot at (1,1).

On a computer screen, a blinking pixel at (1,1) can impart the same
information. If we "zoom in" to that pixel on the computer screen, the
display will remain - a blinking pixel. (unless we exceed the computer's
display resolution, which I imagine depends on the computer's numerical
capabilities.)

BTW, although we are usually interested in the graph of the solution of
y=x^2/(x-1) over a region of the plane, and therefore draw the hollow
dot at (1,1), we should realize that the division by x-1 affects the
whole plane - ie the whole line x=1 is 'removed'. Maybe the easiest way
So, for y=x^2/(x-1), what about (2,4)? It satisfies the equation - ie
'true', What about (2,3)? - it generates 'false'. What about (1,1)? And

Gary Tupper

Date Subject Author
11/21/13 Jerry P. Becker
11/21/13 Dave L. Renfro
11/21/13 Gary Tupper
11/25/13 Gary Tupper
11/25/13 Robert Hansen
11/25/13 Gary Tupper
11/25/13 Robert Hansen
11/25/13 Robert Hansen
11/25/13 Joe Niederberger
11/21/13 Robert Hansen
11/24/13 Joe Niederberger
11/25/13 Robert Hansen
11/25/13 Joe Niederberger
11/25/13 Joe Niederberger
11/25/13 Robert Hansen
11/25/13 Joe Niederberger
11/25/13 Robert Hansen
11/25/13 Robert Hansen
11/25/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Robert Hansen
11/26/13 Robert Hansen
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Louis Talman
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Gary Tupper
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Robert Hansen
11/26/13 Joe Niederberger
11/26/13 Joe Niederberger
11/26/13 Joe Niederberger
11/27/13 Joe Niederberger
11/27/13 Robert Hansen
11/27/13 Joe Niederberger
11/27/13 Robert Hansen
11/27/13 Joe Niederberger
11/27/13 Robert Hansen
11/27/13 Joe Niederberger
11/28/13 Robert Hansen
11/27/13 Joe Niederberger
11/28/13 Joe Niederberger
11/28/13 GS Chandy
11/28/13 Joe Niederberger
11/29/13 Robert Hansen
11/28/13 Joe Niederberger
11/29/13 GS Chandy
11/29/13 Joe Niederberger
11/29/13 Joe Niederberger
11/29/13 Robert Hansen
11/29/13 Joe Niederberger
12/4/13 GS Chandy
12/4/13 Joe Niederberger
12/11/13 Joe Niederberger
12/11/13 Robert Hansen
12/11/13 GS Chandy