Re: infinity

stephen@xxxxxxxxxx said:
>> The question was about 'points'. Are second level infinitesimals
>> points or not? They apparently are located on your number
>> line between other points.
>
Tony Orlow (aeo6) wrote:
> Second level infinitesimals are to points what points are to lines.
> They are -1 dimensional entities, and infinity of which make up a point.
>
stephen@xxxxxxxxxx said:
>> So were you wrong when you claimed that .999...999 is the
>> last point between 0 and 1 that is less than 1?
>
Tony Orlow (aeo6) wrote:
> It is the last whole point.

Huh. An infinite number of infinitesimals make up a "whole" point.
Yet you've stated previously that points have no (zero) width.
So presumably these infinitesimals must also have no width.
But the very name "infinitesimal" implies they are somehow larger
than zero (even if only infinitesimally larger). What gives?

Or perhaps I'm confused and you previously stated that points have
widths larger than zero? If so, how wide is a point (the whole
kind, not the infinitesimal kind)?

.

Relevant Pages

  • Re: infinity
    ... > Tony Orlow wrote: ... >> Second level infinitesimals are to points what points are to lines. ... > Yet you've stated previously that points have no (zero) width. ...
    (sci.math)
  • Re: infinity
    ... >> just dipped your toe into the second level of infinitesimals. ... Second level infinitesimals are to points what points are to lines. ... negative dimensional objects. ...
    (sci.math)
  • Re: Is a line segment composed of points?
    ... zero is not the opposite or counterpart for infinity, ... So, the boundaries of objects are curved, but objects themselves are ... my earlier post, since a point has zero extent in all dimensions, it ... rational numbers can represent infinitesimals, ...
    (sci.math)
  • Re: Is a line segment composed of points?
    ... hence it can't be a building block for a finite extent line segment. ... imaginary objects of zero width, ... my earlier post, since a point has zero extent in all dimensions, it ... Rational numbers should be enough to represent the infinitesimals, ...
    (sci.math)
  • Re: Is a line segment composed of points?
    ... hence it can't be a building block for a finite extent line segment. ... imaginary objects of zero width, ... my earlier post, since a point has zero extent in all dimensions, it ... Rational numbers should be enough to represent the infinitesimals, ...
    (sci.math)