Re: Review of Mueckenheims book.

In article <1173449054.506768.280680@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

On 8 Mrz., 22:46, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
mueck...@xxxxxxxxxxxxxxxxx wrote:

WM, you don't disagree that there are infinite sets containing just
finite values, such as the reals in [0,1], are you? I certainly agree
that an infinite set of naturals must contain infinite values, but
that's only because they are spaced apart by a unit in value. Isn't tat
your thinking?

If you disregad physical restrictions, then there are infinitely many
real numbers in the interval.


We do! There are!

Their cardinality, however, is not
larger than "infinite" for any set.

Then show us your claimed bijection between the set of naturals and the
set of reals, as having the same cardinality, as you claim, requires by
definition the existence of such a bijection.




If you take into account the physical restrictions, then there is no
infinite set. And that is the only correct approach.

Maybe in WM's pedantics but not in our mathematics.
.

Relevant Pages

  • 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. ... don't have a definition for an arbitrary set of its "standard ordering" ...
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  • Re: Calculus XOR Probability
    ... you had said that the existence ... 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. ... The equality between element count and value in the naturals holds in the infinite case, showing clearly that the set is only actually infinite when it contains infinite values. ...
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  • 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 ...
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  • 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)
  • 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. ... you had said that the existence ... 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. ...
    (sci.math)
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