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: Non-Euclidean Arithmetic
Replies: 33   Last Post: Sep 21, 2012 2:48 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Paul A. Tanner III

Posts: 5,920
Registered: 12/6/04
Re: Non-Euclidean Arithmetic
Posted: Sep 12, 2012 3:26 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wed, Sep 12, 2012 at 1:03 PM, Joe Niederberger <niederberger@comcast.net> wrote:
> PT III says:
>>Take a standard x-axis and y-axis in the Cartesian plane, and for sake of simplicity, name the points on these lines according to the fact they are each a real number line. Then:
> [etc. etc. etc.]
>
> But I just explained that most reals (with probability 100%) have no names. - there's a problem here.
>


The term can be used in more than one way. When I said "name" I meant, for sake of simplicity as I explicitly said, instead of saying (x,0) just say x. That's a type of naming of an arbitrary point on the x-axis.

There is therefore no problem here.

>
> Even for some that have "names' I just couldn't "home in" on them.


So what? You talk as if you have not heard of "without loss of generality" - look it up. It's standard in mathematics. (I used it a number of times when proving theorems during obtaining my math degree and when teaching geometry. By the way, what degree or degrees do you have? What's your training in mathematics?)

Look at it again - in fact, it's a proof of the following theorem using "without loss of generality": Given real number (point) 1 and any two positive real numbers (points) a and b, we can construct the exact location of real number (point) ab on the real number line:

Connect 1 on the x-axis to b on the y-axis, and, parallel to that drawn line segment, connect a on the x-axis to the y-axis, and this point on the y-axis is ab. That is, in terms of distance from 0 or magnitude or absolute value: ab is to b as a is to 1 - that is, written in terms of ratios or proportions: ab:b as a:1.

And via commutativity we have the other way as an alternative:

Connect point 1 on the x-axis to point a on the y axis, and, parallel to that drawn line segment, connect b on the x-axis to the y-axis, and this point on the y-axis is ab. That is, in terms of distance from 0 or magnitude or absolute value: ab is to a as b is to 1 - that is, written in terms of ratios or proportions: ab:a as b:1.

Note: Your "home in on" talk and your need to name things says that you really need to learn about "without loss of generality" before you speak on this again.

>
> It looked like a process, smelled liked a process, but there's just no carrying it out in general.
>


It's a process.

It is as I said: You are disallowing whatever uses of terms like "process" to satisfy your preconceived conclusions.


Date Subject Author
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
Wayne Bishop
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
kirby urner
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/12/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/12/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/12/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/13/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/13/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/13/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/13/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/14/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/13/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/13/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/13/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/13/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/14/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/16/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/17/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/14/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/17/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/15/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/17/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/15/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/17/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/18/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/20/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III
9/20/12
Read Re: Non-Euclidean Arithmetic
Joe Niederberger
9/21/12
Read Re: Non-Euclidean Arithmetic
Paul A. Tanner III

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.