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Re: Matheology § 008
Posted:
May 16, 2012 11:51 PM
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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:
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> > 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:
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> > > > On May 16, 11:49 pm, "|-| E R C" <herc.of.z...@gmail.com> wrote:
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> > > > > On May 17, 12:11 pm, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > On May 16, 5:27 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
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> > > > > > <snip>
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> > > > > > > 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!
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> > > > > > > ****YOU****
> > > > > > > We are agreed there is no bijection between N and R.
> > > > > > > So card(R) > card(N)
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> > > > > > Correct. You only need WU for this.
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> > > > > > From WU we get immediately that there is no bijection from
> > > > > > N to P, where P is the set of all infinite digit strings.
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> > > > > > card(P) > card(N) follows immediately from the definition of
> > > > > > cardinality,
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> > > > > > - William Hughes
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> > > > > Right!
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> > > > Ok we have card(P) > card (N)
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> > > > Now just show card(P) = card(R) (hint look for a surjection and and
> > > > injection)
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> > <snip new argument>
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> > We agree that card(P) > card(N) (at least in a mathematical sense).
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> huh? If my carton of beer is missing a 6 pack that doesn't mean
> Fruitology(stubbies) > Fruitology(cans)
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> Herc
No, but if every list of infinite digit strings is missing an infinite
digit string this does mean card(P) > card(N).
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