Re: infinity

David R Tribble said:
> 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?
Infinitesimal means essentially zero, but conceptually not nothing. It's the
same thing as saying that finite numbers represent something real, but adding
them to an infinite number has no effect.
>
> 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)?
>
>
If you ask most people what infinity times zero is, they answer zero. It seems
plenty intuitive for most people to suppose that adding points forever will
never make anything larger than a point. So, why does it bother you to imagine
such a thing? Points are zero in size, but just as there are many levels of
infinity, therre ar equally many levels of zero. Zero and infinity are two
sides of the same coin.
--
Smiles,

Tony
.

Relevant Pages

  • Re: Is a line segment composed of points?
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  • Re: Is a line segment composed of points?
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    (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, ...
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  • Re: Calculus XOR Probability
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