[SPORK, FUNNY] Donald Rumsfeld... the poet?
R. A. Hettinga
rah at shipwright.com
Mon Apr 14 20:57:17 PDT 2003
--- begin forwarded text
From: Somebody Piled Math Higher and Deeper at MIT
To: "R. A. Hettinga" <rah at shipwright.com>
Subject: Re: [SPORK, FUNNY] Donald Rumsfeld... the poet?
Date: Sun, 13 Apr 2003 17:22:39 -0400
Bob,
At first thought, that the "finitely describable reals" should be countable
seems correct. Only finitely many statements of a given length possible, so
list them all in order of length, and the list should provide a counting,
QED.
But why is e one? Or pi? For proper definition they both require a
limiting process.
And once limits are allowed into the class of processes of finite
describability, the camel's nose is under the tent. Because every real
number is the limit of some sequence of rational numbers. And the Cantor
diagonal construction shows easily that any listing of those is not
complete.
So, you must accept that either the finitely describable numbers are
uncountable or that they include some that are easily named.
Which it is probably depends on the exact definition you choose for
"finitely describable number."
<Somebody>
----- Original Message -----
From: "R. A. Hettinga" <rah at shipwright.com>
To: "Philodox Clips List" <clipsi at philodox.com>
Sent: Sunday, April 13, 2003 3:14 PM
Subject: Re: [SPORK, FUNNY] Donald Rumsfeld... the poet?
>
> --- begin forwarded text
>
>
> From: "Russell Turpin" <deafbox at hotmail.com>
> To: fork at xent.com
> Date: Sun, 13 Apr 2003 18:28:22 +0000
> Subject: Re: [SPORK, FUNNY] Donald Rumsfeld... the poet?
> List-Subscribe: <http://xent.com/mailman/listinfo/fork>,
> <mailto:fork-request at xent.com?subject=subscribe>
> Sender: fork-bounces at xent.com
>
> >As we know,
> >There are known knowns.
> >There are things we know we know.
> >We also know
> >There are known unknowns.
> >That is to say
> >We know there are some things
> >We do not know.
> >But there are also unknown unknowns,
> >The ones we don't know
> >We don't know.
> >-Feb. 12, 2002, Department of Defense news briefing
>
> This reminds me of the shy reals. We all know
> Cantor's diagonalization argument that the
> cardinality of the reals is qualitatively
> greater than the cardinality of integers. So
> we say the integers are countable, while the
> reals are not. The rationals are also countable.
> As are the algebraic numbers, which include
> many (though only a countable number) if
> irrationals, such as sqrt(5) and cuberoot(3).
> Of course, there are plenty of real numbers that
> aren't algebraic that we can describe by other
> methods, such as pi, and e.
>
> But here's the interesting thing: all the
> finitely describable numbers are themselves
> countable. The remaining reals, the "shy"
> ones, are the uncountable bulk of reals, even
> though I cannot name one of them.
>
>
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> --
> -----------------
> R. A. Hettinga <mailto: rah at ibuc.com>
> The Internet Bearer Underwriting Corporation <http://www.ibuc.com/>
> 44 Farquhar Street, Boston, MA 02131 USA
> "... however it may deserve respect for its usefulness and antiquity,
> [predicting the end of the world] has not been found agreeable to
> experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire'
>
--- end forwarded text
--
-----------------
R. A. Hettinga <mailto: rah at ibuc.com>
The Internet Bearer Underwriting Corporation <http://www.ibuc.com/>
44 Farquhar Street, Boston, MA 02131 USA
"... however it may deserve respect for its usefulness and antiquity,
[predicting the end of the world] has not been found agreeable to
experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire'
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