Virgil
Posts:
7,011
Registered:
1/6/11


Re: Matheology � 263
Posted:
May 17, 2013 2:08 AM


In article <9d6b39cdb3494d9ba34ea759e81cb4ff@ul7g2000pbc.googlegroups.com>, Graham Cooper <grahamcooper7@gmail.com> wrote:
> On May 17, 11:51 am, Virgil <vir...@ligriv.com> wrote: > > In article > > <3fb4082ca45547a8a931c219fd2fb...@qc10g2000pbb.googlegroups.com>, > > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > > > > > > > > > > > > > > > On May 17, 10:57 am, Virgil <vir...@ligriv.com> wrote: > > > > > OK, use > > > > > > > f(1) = { 1 , 3 , 6 } > > > > > f(2) = { 1 , 5 , 11 } > > > > > f(3) = { 2 , 4 , 6, 8 , 10 , ... } > > > > > f(4) = { 4 , 5, 6, 7, 8 } > > > > > > > f(n) = N  n>4 > > > > > > > What is set S? > > > > > > Note that there are only 5 subsets of N that ARE in the image of your > > > > 'f' out of uncountably many subsets of N to chose from that will be > > > > S's, i.e., subset of N but not values of f. > > > > > > They are > > > > every finite subset of N having > > > > less that 3 members > > > > or exactly 4 members, > > > > or more than 5 members, > > > > or containing either 2, or a natural larger than 8, > > > > and every infinite subset of N other than f(3) and N. > > > > > > Take your pick. > > > > ` > > > > So Cantor's Method does not work?
Since there are far more sets not in the image of any function from N to 2^N than in its image, why are you so hot to get one in particular? > > Your method (white box inspection) does not work for every possible f, > as such it is of no consequence.
Name one it does not work for! > > GIVEN A SPECIFIC f, WHAT IS CANTORS MISSING SET?
If you could pick a subset of N at random, it would almost certainly not be in the image of any randomly chosen function. > > All your answers are wrong! They are not in the image of the function you presented, which is all they are asked to be. 

