Search All of the Math Forum:

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

Topic: Matheology § 008
Replies: 15   Last Post: May 17, 2012 12:37 AM

 Messages: [ Previous | Next ]
 William Hughes Posts: 1,555 Registered: 12/7/10
Re: Matheology § 008
Posted: May 16, 2012 11:51 PM

On May 17, 12:39 am, "|-| E R C" <herc.of.z...@gmail.com> wrote:
> On May 17, 1:36 pm, William Hughes <wpihug...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On May 17, 12:29 am, "|-| E R C" <herc.of.z...@gmail.com> wrote:
> > > On May 17, 12:56 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > On May 16, 11:49 pm, "|-| E R C" <herc.of.z...@gmail.com> wrote:
>
> > > > > On May 17, 12:11 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > > On May 16, 5:27 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > > > > <snip>
>
> > > > > > > Using WU only, which is viable, given a particular L = R1, R2, R3...
> > > > > > > L is missing_an_infinite_digit_string
> > > > > > > and in a mathematical sense incomplete!

>
> > > > > > > ****YOU****
> > > > > > > We are agreed there is no bijection between N and R.
> > > > > > > So card(R) > card(N)

>
> > > > > > Correct.  You only need WU for this.
>
> > > > > > From WU we get immediately that there is no bijection from
> > > > > > N to P, where P is the set of all infinite digit strings.

>
> > > > > > card(P) > card(N) follows immediately from the definition of
> > > > > > cardinality,

>
> > > > > >                  - William Hughes
>
> > > > > Right!
>
> > > > Ok we have card(P) > card (N)
>
> > > > Now just show card(P) = card(R)   (hint look for a surjection and and
> > > > injection)

>
> > <snip new argument>
>
> > We agree that card(P) > card(N)  (at least in a mathematical sense).
>
> huh?  If my carton of beer is missing a 6 pack that doesn't mean
> Fruitology(stubbies) > Fruitology(cans)
>
> Herc

No, but if every list of infinite digit strings is missing an infinite
digit string this does mean card(P) > card(N).

Date Subject Author
5/15/12 mueckenh@rz.fh-augsburg.de
5/15/12 Graham Cooper
5/15/12 William Hughes
5/16/12 Graham Cooper
5/16/12 Graham Cooper
5/16/12 William Hughes
5/16/12 Graham Cooper
5/16/12 William Hughes
5/16/12 |-| E R C
5/16/12 William Hughes
5/16/12 |-| E R C
5/16/12 William Hughes
5/16/12 |-| E R C
5/16/12 William Hughes
5/17/12 Graham Cooper
5/16/12 |-| E R C