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 ]
Joe Niederberger

Posts: 3,079
Registered: 10/12/08
Re: Visual Presentation of Real Number System
Posted: Nov 29, 2013 11:27 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

>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

That is fine for sequences series that converge to a computable number. Any real can be viewed as the limit of a sequence of of rationals. While each of those rationals is computable, the sequence itself, generally, is not.

The problem is "sloppy talk that fails to distinguish the mathematical from the heuristic, the picturesque, the realm of applied from the realm of the math itself."

The problem here is "choose" or "pick" -- no one can do that for a random real. To pick or choose means to distinguish one from the rest. A description of what such a number would sort of look like, or what some of its properties would have to be, as you gave, even if completely formal, does not distinguish one random real from all the rest.

There is no mathematization of the "dart" or the actions performed with the dart, that can do the job either. Its an ill-formed statement, a fantasy that exists neither in the real world in in the world of mathematics.

R Hansen says:
>Using physics metaphorically is not a problem, when, as you stated, it is done by a mathematically mature person.
&
>I still am not sure what your issue is.

My issue is, that in the world of probability, there is a
"echo" of the confusion between real-world stuff similar to the way some students may be confused between pictures, and the math that lies behind the picture. With probability though, it also has to do with notions of time and action. My claim, such as it is, is I think its harder for many writers on probability matters to keep those two worlds separate and clear in their writing, in their teaching.

I wasn't accusing you of being similarly confused.
As far as the author of that link I posted, while he may not be internally confused, his writing style doesn't help others see the truth. He persists with the "zero probability events happen all the time" meme.

I think greater efforts to mentally separate those two worlds would help the world of mathematical teaching. I wouldn't expunge those real world metaphors any more than I would expunge pictures, just make sure everyone knows which is which.

And, as I said, I was having some fun here. If you came up with your ideas about particular (computable) numbers and non-particular numbers on the spot in this discussion, then congratulations, and I hope you had some fun too.

Cheers,
Joe NM


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.