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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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Paul

Posts: 474
Registered: 7/12/10
Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado

Posted: Nov 4, 2013 10:11 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Monday, November 4, 2013 2:43:37 PM UTC, David Hartley wrote:
> In message <8933482d-8920-46ce-8886-6402fce0cea2@googlegroups.com>, Paul
>
> <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
>
> >equality I'm complaining about doesn't follow _immediately_. However,
>
> >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.
>
>


Many thanks for this interesting example. However, your acknowledgement that you haven't used the specific B defined in the paper is critically important.

I think that our understanding of the issues remains at the same place that it was when I made my last post. We understand that the equality at issue doesn't follow _immediately_. But we don't know whether it follows or not.

In order to get a counter-example to show that the equality at issue doesn't follow, we need the equality statement to be false, and we also need to use a set B which is consistent with the author's construction.

I still prefer to work with the author's definition. For reasons given earlier, I'm very sceptical of the idea that the author's definition of L is different from what he intends.

[Please please don't take the above to mean that I don't appreciate your work. I'd love to resolve this and I thank you heartily for working with me on this.]

Paul Epstein



Date Subject Author
11/3/13
Read Surprise at my failure to resolve an issue in an elementary paper by Rado
Paul
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/3/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Peter Percival
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/5/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/6/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/6/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
David Hartley
11/8/13
Read Re: The Rado paper -- a possible further simplification
Paul
11/8/13
Read Re: The Rado paper -- a possible further simplification
David Hartley
11/7/13
Read Re: Another not-completely-insignificant gap in the Rado paper
Paul
11/7/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
fom
11/8/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/8/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey
Theorem that goes far beyond omitting proof steps
Paul
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey
Theorem that goes far beyond omitting proof steps
Paul
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
David Hartley
11/10/13
Read Re: Possible major blunder in Rado's version of Canonical Ramsey
Theorem that goes far beyond omitting proof steps
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Paul
11/4/13
Read Re: Surprise at my failure to resolve an issue in an elementary paper
by Rado
Peter Percival

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