Re: Calculus XOR Probability

Brian Chandler said:
Sometimes you seem to agree that (for example) the sequence of pofnats
(0, 1, 2, ...) has no end, and almost always you agree it has no
well-defined end. You say this means it "has no well defined size", yet
you (now) say you advocate "a more numeric approach to infinity", which
appears to mean you insist it must have a "size". It doesn't bother you
that these two claims appear to contradict each other?


Tony Orlow wrote:
It doesn't bother me that they appear to YOU to contradict each other. I have
repeatedly said that the unboundedness of the finites poses problems for
measuring the set of finite naturals, and that no real size can be attributed
to this set. However, if we say that there is a specific infinite number of
reals in each unit interval, and that there is an equally infinite number of
unit intervals on the real line, then we have a cohesive system consistent with
rules governing finite sets of such values, namely, the Inverse Function Rule.

If your "Inverse Function Rule" means that for every "unit interval on
the real line" corresponding to some natural k that there is an
corresponding "inverse" real x in each "unit interval" such as (0,1],
then this is simply the mapping:
x = 1/k for all k=1,2,3,...
k = 1/x for all x in (0,1].

But this mapping denumerates only some of the reals (0,1] and omits
a much larger number of them completely (e.g., x=2/3). So you can't
use this mapping to say that the number of reals in a unit interval is
the same as the number of unit naturals on the real line.

.

Relevant Pages

  • Re: Calculus XOR Probability
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  • Re: Calculus XOR Probability
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  • Re: An uncountable countable set
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    (sci.math)
  • Re: An uncountable countable set
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  • Re: Calculus XOR Probability
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    (sci.math)