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Topic: Surprise at my failure to resolve an issue in an elementary paper by Rado
Replies: 44   Last Post: Nov 10, 2013 12:23 PM

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 David Hartley Posts: 463 Registered: 12/13/04
Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
Posted: Nov 4, 2013 9:43 AM

<pepstein5@gmail.com> writes
>Agreed. The redefinition of L leads to problems soon after (3) of page
>3. Furthermore, assuming an error in a paper should be a last resort.
>An author is far more likely to omit steps of reasoning than to make an
>elementary logical error. My initial post merely shows that the
>just because an assertion doesn't follow immediately doesn't mean that
>it doesn't follow. To show that it doesn't follow, we would need a
>counter-example and I haven't seen one.

To avoid all the tedious notation, let's define

D(x,y,i) to mean x and y are subsets of B with r elements which, when
ordered by <, differ only at the position indexed by i.

The original definition of L has i in L iff

for all x,y D(x,y,i) -> f(x) =/= f(y)

The problematic step in the proof assumes that if i is *not* in L then

for all x,y D(x,y,i) -> f(x) = f(y)

Suppose for a counter-example, that B = N and put r = 2 and

f(x) = 2^(1 + min x) if max x is even
= 3^(1 + min x) if max x is odd

Then L = {0} with the original definition but is empty with the
suggested variation.

It may be that with the specific B defined in the paper the two
properties are equivalent but it certainly requires proof.

--
David Hartley

Date Subject Author
11/3/13 Paul
11/3/13 David Hartley
11/3/13 fom
11/3/13 fom
11/3/13 fom
11/4/13 fom
11/4/13 Paul
11/4/13 Paul
11/4/13 Peter Percival
11/4/13 David Hartley
11/4/13 Paul
11/4/13 David Hartley
11/4/13 Paul
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11/5/13 David Hartley
11/5/13 Paul
11/5/13 David Hartley
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11/6/13 Paul
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11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/7/13 David Hartley
11/7/13 Paul
11/7/13 David Hartley
11/8/13 Paul
11/8/13 David Hartley
11/7/13 Paul
11/7/13 fom
11/8/13 Paul
11/8/13 David Hartley
11/10/13 Paul
11/10/13 David Hartley
11/10/13 Paul
11/10/13 David Hartley
11/10/13 David Hartley
11/10/13 Paul
11/4/13 Paul
11/4/13 Peter Percival