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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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 fom Posts: 1,968 Registered: 12/4/12
Re: Surprise at my failure to resolve an issue in an elementary paper

Posted: Nov 3, 2013 10:09 PM

On 11/3/2013 8:26 PM, David Hartley wrote:

>
> 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.
>

And, we define sets how?

{ x | P(x) }

to interpret "whenever ... then" as a conditional.

I see that you also used an existential quantifier in your
first assessment of the definition.

P(k) <-> (

k in { 1, ..., r }

/\

AmAn(

[ ( ( < m > = < a_1, ..., a_r > /\ < n > = < b_1, ..., b_r > )

/\

( m subset B' /\ n subset B' ) )

/\

Ai( ~( i = k) <-> ( a_i = b_i ) )

/\

( a_k = b_k ) )

->

f( m ) =/= f( n ) ]

) )

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