Re: abundance of irrationals!) - rectangles of area 1.bmp [0/1]
- From: Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx>
- Date: Tue, 10 May 2005 16:42:18 -0600
In article <MPG.1ceade5d14cae722989c06@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> I already stated that maintaining finiteness as a property is not valid over
> an
> infinite series of constantly increasing values, based on what we know about
> infinite series and their sums. You counter that induction only proves things
> for finite series
WRONG! Orlow again conflates the finiteness of a sequence or series with
the finiteness of its members. he makes the same mistake with sets.
The members of any sequence of numbers are all finite, regardless of
whether the sequence itself has a last member, and so is finite, of not.
The set of reals between 0 and 1 is infinite even though every member of
that set is finite. Similarly for the set of rationals {1/n: n in N},
the members of the set are all finite unit fractions, but there are more
thatn any finite number of them in that set.
.
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