fom
Posts:
1,968
Registered:
12/4/12


Re: Surprise at my failure to resolve an issue in an elementary paper by Rado
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) }
Paul is correct about the quantifier and wrong about failing 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 ) ]
) )

