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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

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 Wally W. Posts: 283 Registered: 6/15/11
Re: the ugly contradiction at the heart of High School Geometry #35.3 Uni-text 8th ed.: TRUE CALCULUS
Posted: Nov 2, 2013 3:53 PM

On Fri, 1 Nov 2013 14:00:29 -0700 (PDT), Archimedes Plutonium wrote:

>the ugly contradiction at the heart of High School Geometry #35.3 Uni-text 8th ed.: TRUE CALCULUS
>
>On Friday, November 1, 2013 4:23:16 AM UTC-5, Wizard-Of-Oz wrote:

>> Archimedes Plutonium <plutonium.archimedes@gmail.com> wrote in
>>
>>

>
>>
>>
>> There is no empty space between the points that lie on a line in
>>
>> geometry.  None.
>>
>>
>>
>>
>>

>> > So you have Point, Empty Space,
>>
>> > Next Point, which gives the line its length.
>>
>>
>>
>> Nope.  That's not geoemtry.
>>

>
>Someone said this fool of Wizard of Oz is Eric Gisse. Can someone verify?
>
>Now I do not write this to teach a fool for they are unteachable.
>
>I write this for the readers that know logic. That know a contradiction when it is pointed out.
>
>So you have in Old Geometry that a line is a set of points, and that points are without length, without width and without depth. But you are told a line has length. So how can a line have length if points never have length?

So Zeno's arrow can't exist. It could never hold together in flight
because it is not continuous.

>Well that is a logical contradiction.
>
>The only remedy is to insert empty-space between one point and its successor point.

Define a "successor point".

Is the 44th President of the USA a successor to George Washington?

How many Presidents were there between?

Why do you think a "successor point" must be adjacent to and touching

What is the length of the shortest line segment in a Koch snowflake?
https://en.wikipedia.org/wiki/Koch_snowflake

Koch curve.

Let us know when you identify the shortest line segment. Please post
the coordinates of its endpoints.

>The Naturals have length because the distance between 0 and 1 or 1 and 2 is empty space of 1 unit distance. The length of 0 to 2 is 2 because of 2 units of empty space.
>
>So in Old Geometry, their entire subject was deeply, internally flawed, all because they never had **empty space** between successor points.

Space need not be empty between "successor points."

There may or may not be space between successive, discrete items of
finite size. There is always space between such items unless they are
touching. The space between them need not be empty; it can be filled
with other items. The Presidential office was not empty for all the
time between George Washington and now.

For "successive" points of infinitesimal size in a geometer's line:
there is always space between successive points, and it that space is
never empty.

>And the way to remedy or solve "What is empty space?"

This question has a false premise. Your string of words has the proper
English syntax to form a "question," but it is nonsense in this
context.

Empty space does not exist in a geometer's line.

>is to find out what the borderline is between finite and infinite, such as 10^603 which thus makes 10^-603 the microinfinity and the smallest empty space.

Are you aware of IEEE binary128 quadruple precision numbers, which can
be used to manipulate values greater than 10^603?

>So, a fool like the above poster will never learn anything but the hatred he wallows in;

Who is mentioning hatred? Is this projection?

>but the reader who is objective and a modicum of logic will instantly understand how High School and College Geometry is a sewer of contradiction and how much of a fool they themselves were for sucking in that contradiction rather than protest to the teacher that to have real geometry, you need Point, Empty Space and Line.

What is "real geometry"?