Re: Is continuum completely filled up?

toshiaki <farawfu@xxxxxxxxx> writes


What I intended to say, is wheather a line is build from points or not.
Why point of measure 0 gather up to produce measure or lengh?

Sticking my head over the parapet again ...I can't see how you can make
up something continuous from something point like, however many points
you have.

If any 2 real numbers are different, there is a gap between them,
in which of course there is another real. But there are also now
2 gaps. So while there are an infinite number of reals
there must also be an infinite number of gaps? Or is this fallacious
because implicit in this type of construction of the reals is a
countably infinite process?

--
Andy Smith
.

Relevant Pages

  • Re: Is continuum completely filled up?
    ... So while there are an infinite number of reals ... there must also be an infinite number of gaps? ... But the same is true of the rationals. ...
    (sci.math)
  • Re: Is continuum completely filled up?
    ... Andy Smith wrote: ... So while there are an infinite number of reals ... there must also be an infinite number of gaps? ...
    (sci.math)
  • Re: Is continuum completely filled up?
    ... So while there are an infinite number of reals ... there must also be an infinite number of gaps? ... The depth of that tree is countably infinite. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... If a quantitative set is mapped in ascending order from the naturals, ... number of reals on the line. ... to the subsequent logic that claims such a set cannot have infinite values. ... standard orderings, since sets in general don't come with little tags ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... If a quantitative set is mapped in ascending order from the naturals, with each increment in the domain, the range increases by some amount. ... Like it's the number of unit intervals, and the number of reals in the unit interval. ... You are using a form of infinite induction, making a claim for an infinite set based on all finite initial segments of it. ... don't have a definition for an arbitrary set of its "standard ordering" ...
    (sci.math)