Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Joe Niederberger Posts: 4,657 Registered: 10/12/08
Re: Visual Presentation of Real Number System
Posted: Nov 27, 2013 5:33 PM

R Hansens says:
>That is why I came up with the decimal digits approach.

You mean this?

(R Hansen)
>Given a hypothetical process that selects real numbers entirely at random, the numbers thus selected are always of the "undeterminable" type. Essentially, think of a number with an infinite and entirely random sequence of decimal digits. Determinable numbers can have an infinite sequence of decimal digits, but the digits are never entirely random, since they are constrained by the function that creates the number.

That's a nice informal description of the difference between a computable number and a computable one.

But -- now describe a process that "selects" that non-computable number. The best I could come up would be
a Geiger-counter driven digit generator. But it would never get to the end of that first number. That "dart" would never really reach the board! So saying "pick a random real ...." really hides quite a bit of sisyphean effort.

Cheers,
Joe N

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