Re: infinity


Tony Orlow (aeo6) wrote:
> imaginatorium@xxxxxxxxxxxxx said:
> >
> > Tony Orlow (aeo6) wrote:
> > > Jiri Lebl said:
> > > > Tony Orlow (aeo6) wrote:
> > > > > By the same token, to say that all strings in the language are finite is to say
> > > > > that there is some finite natural number K such that all characters in any
> > > > > string can be enumerated by the natural numbers {1,2,...,K}. So, let S and T be
> > > > > strings constructed by concatenting K characters:
> >
> > Of course this is nonsense. By another token, to say that all people
> > have a mother is to say that there is some mother M such that all
> > people can be enumerated as the children of M. So what's her name?
> >
> > Look, when _we_ say "all strings in the language are finite" we mean:
> >
> > (1) For all S (string in language), exists n s.t. n > len(S)
> >
> > Why do you insist this is the same as saying:
> >
> > (2) Exists K s.t. for all S (string in language), K > len(S)
> >
> > While claiming not to have QD?
> >
> > Brian Chandler
> > http://imaginatorium.org
> >
> >
> Why do you not respond to the post that I was responding to, from which I took
> the very same language? Oh, that's right, he's on your side. All I did was turn
> his argument back on him, almost verbatim, ...

Ah, well, "almost verbatim". Therein lies the rub - in the difference
between a mathematician and a salad chef. Famously, the astronomer said
"Ah, all sheep in Scotland are black", the physicist said "There is
empirical evidence that many sheep in Scotland are black", and the
mathematician said, "In Scotland there exists at least one sheep, at
least one side of which is black". Less famously, the salad chef said
"Scotland exists at least, one side in there one sheep at least exists
of which is black there."

(Get Ross Finlayson to explain it to you if you're lost. Hmm, that's a
masterful idea, if I say so myself. sci.math would go quiet for a few
days, and you'd be the one with the headache.)

Brian Chandler
http://imaginatorium.org

.

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