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: the ugly contradiction at the heart of High School Geometry #35.3
Uni-text 8th ed.: TRUE CALCULUS

Replies: 24   Last Post: Nov 3, 2013 7:44 PM

 Messages: [ Previous | Next ]
 Wally W. Posts: 283 Registered: 6/15/11
Re: what a real rebuttal of AP's claim of a contradiction in the heart of Geometry looks like #35.9 Uni-text 8th ed.: TRUE CALCULUS
Posted: Nov 3, 2013 12:42 AM

On Sat, 2 Nov 2013 20:35:41 -0700 (PDT), Archimedes Plutonium wrote:

>On Saturday, November 2, 2013 9:26:15 PM UTC-5, Wally W. wrote:

>(snipped)

>> Are we having fun yet?
>
>I am because you show how crippled in mind the establishment mathematics is:
>
>---------------------------------------
>AP Claim:
>
>(1) point has no distance, no width, no depth
>(2) line has distance but no width and no depth
>
>Contradiction: because a line composed of just points, all of which have no distance, or 0 distance when added up yields 0 distance.
>
>How to correct the Contradiction? Find the finite to infinity borderline which gives a microinfinity which acts as "empty space between two successive finite points" thus giving the two points a distance. So that a line in Geometry, True Geometry is a finite point with empty space and then the next finite point with empty space and then the next finite point with empty space for however distant that line is.
>
>Distance is a measure of one point to another point because distance is point A, then empty space, then point B.
>
>
>--------------------------------------------
>
>Now Wally is incapable of a paragraph or longer rebuttal, for he can only handle short sentences and cannot form a rebuttal argument. So based on what Wally said above, here is his defense of the Establisment Geometry.
>
>
>What a Wally Walrus rebuttal is beginning to look like:
>
>(1) point has no distance, no width, no depth
>(2) line has distance but no width and no depth
>
>
>WW > They (points) don't *become* more dense. They always existed. How do you

>>
>> *create* points? From what do you create them?

>
>WW > A length is associated with any distance between points, continuous or

>>
>> not.

>
>WW > So Zeno's arrow can't exist. It could never hold together in flight

>>
>> because it is not continuous.
>>

>
>So apparently a line for WW is continuous.

Yes.

Consider the line y = 2 * x

Please provide an x value at which this line is not continuous.

if your points are 10^-603 units apart (does this work for both
light-years and microns, you never explained), then is this line not
continuous at x = 1 + (0.0001) * (10^-603)? Is there empty space at
this x value?

>So the flaw remains, and the contradiction remains because the distance between point A and point B is not tallied by how many other points are in the path of the distance but how much empty space resides between the 2 points in question.

The distance between Point A and Point B is given by the Pythagorean
Theorem, regardless of how many points exist between these two points.

>So Wally is confused in thinking that distance is totally separate from length, when in fact it is a chose of words, whether we want to call it distance or want to call it length.

Consider the diameter of a circle. The separation between the ends of
a diameter a distance. It is not a length along the circumference of
the circle.

>So Wally still has failed to defend establishment Geometry, for he needs to offer a mechanism of how points can turn from no distance or no length into points having distance and having length. He needs to provide a mechanism.
>
>In the AP argument, the mechanism is the third entity of empty space that is combined with point and line.
>
>
>--------------------------------------------------
>
>Until Wally can provide that mechanism, he has failed to defend.
>
>AP

I'll admit to not having the set theory background to provide a
rigorous proof.

On the other hand, you haven't given the coordinates for the location
of empty space on a line. You say it exists. Why can't you give one
example of where your empty space may be found in any of the infinite
number of lines that can be defined?