Re: How to do magic with infinity

From: Alan Sagan (not_at_this_address_2_at_hotmail.com)
Date: 10/06/04 

Date: 5 Oct 2004 23:50:56 -0700

cafeinst@msn.com (Craig Feinstein) wrote in message news:<b671fc3e.0410050838.49870c69@posting.google.com>...
> Here's an interesting paradox in geometry, if one believes that
> infinity exists.
I think the whole debate rests on what you mean by exists.
For example does a line segment exist? A line segment has one
dimension, and even a line segment drawn on paper has length, width
and height. So a line segment is an abstraction from things we find in
the real world.
Same goes for a point. What about the word 'CAT'? Another abstraction
that conveys the meaning cat but 'CAT' doesn't even look like a cat!
So what does existence mean to you?

>
> Let AB-> be a ray.
>
> A B C
> .------------.-------------.---------->
>
> Remove line segment AB from ray AB->.
>
> A B B C
> .------------. .-------------.----------->
> Relabel the points.
>
> D E A B C
> .------------. .-------------.------------.----------->
> By simply cutting the ray into two parts, we were able to "magically"
> create a new line segment. We started with one ray. Now, we have one
> ray and one line-segment.
The infinity you are using here, the ray, is an abstraction, just like
a line segment. No one in their right mind who teaches/studies
standard geometry would say that a point, line segment, ray, line,
plane actually exist, they are all abstractions. So does the
confusion come from that people don't know that in geometry these
objects that are infinite are just abstractions?

Relevant Pages

  • Re: How to do magic with infinity
    ... For example does a line segment exist? ... Another abstraction ... The infinity you are using here, the ray, is an abstraction, just like ... standard geometry would say that a point, line segment, ray, line, ...
    (sci.math)
  • Freges Implication in Topology, a space now taken
    ... A basic test of the thinker is to begin. ... A segment as the entity will allow a class of function. ... A segment in topology may cause the geometric symbol. ... A space literally the only allowed geometry for symbol's placement. ...
    (sci.logic)
  • Re: Zuhairs Circles
    ... > Please think about a point and a segment, where the segment is a non-composed element. ... and what is potential infinity and actual infinity and why ... mean by" non finite collection" I should guess that the set of all sets ...
    (sci.math)
  • Re: How to do magic with infinity
    ... what you are doing is just laying off a segment end to end and saying you've ... if you truely have an "infinite ray", you cannot cut it, since there is no ... segment and you are really just laying off segments end. ... but it makes no sense to break infinity up into two pieces... ...
    (sci.math)
  • Re: How to do magic with infinity
    ... what you are doing is just laying off a segment end to end and saying you've ... if you truely have an "infinite ray", you cannot cut it, since there is no ... segment and you are really just laying off segments end. ... but it makes no sense to break infinity up into two pieces... ...
    (sci.logic)