
Re: what a real rebuttal of AP's claim of a contradiction in the heart of Geometry looks like #35.9 Unitext 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 UTC5, 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 lightyears 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?

