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Topic: Matheology � 263
Replies: 57   Last Post: May 17, 2013 8:52 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: Matheology § 263
Posted: May 16, 2013 9:13 PM

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).
>
>

Ahhh now we're getting somewhere!

f(5) = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ...... }

f(6) = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ...... }

f(7) = {1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , ...... }

........

i.e

f(n) = N | n>4

Herc

Date Subject Author
5/10/13 Virgil
5/13/13 Virgil
5/13/13 Graham Cooper
5/13/13 Virgil
5/13/13 Graham Cooper
5/13/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/14/13 Graham Cooper
5/14/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/15/13 Virgil
5/15/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Scott Berg
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Graham Cooper
5/16/13 Virgil
5/16/13 Virgil
5/16/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/17/13 Virgil
5/17/13 Graham Cooper
5/14/13 Graham Cooper
5/14/13 Virgil