Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 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 3, 2013 9:26 PM

<pepstein5@gmail.com> writes
>We are given that rho_0 does not belong to L. However, L is defined by
>a "for all" statement. So, for rho_0, the for-all statement is false
>and we can find some yi and yi' to make f(z0, ..., z_r-1) = f(y0,...,
>y_r-1) true.
>
>But the author is stating something much stronger -- that we can deduce
>the equality for an arbitrary yi and yi'.

I've never met Ramsey theory before, so I may also be missing something.
But as far as I can see you are quite correct: this step is a
non-sequitur.

The solution is presumably to redefine L such that the deduction is
valid. Ah! I think this ties in with something you've written in the
interpreting his definition of L in the same way, and I can't see any
other way of reading it. But he presumably intended to define L as the
set of numbers rho < r which have the property

there exist two ordered sets of r numbers differ only at the position
indexed by rho which do not have the same image under f.

(I'm not writing it in his style, what terrible notation.)

More straightforwardly, L is the set of rho < r which do *not* have the
property

whenever two ordered sets of r numbers differ only at the position
indexed by rho, then they have the same image under f.

So for rho_0 not in L the step in question is valid.

--
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
11/4/13 David Hartley
11/4/13 Paul
11/5/13 Paul
11/5/13 David Hartley
11/5/13 Paul
11/5/13 David Hartley
11/5/13 Paul
11/6/13 Paul
11/6/13 Paul
11/7/13 Paul
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