Re: infinity

imaginatorium@xxxxxxxxxxxxx said:
> aeo6 Tony Orlow wrote:
>
> <and wrote and wrote and wrote: snip>
>
> > I claim that there are a finite number of finite strings. I never claimed there
> > were F of them.
>
> Right. So let me guess - there are a *finite number* of them, but this
> finite number (in asterisks) is somehow not like most finite numbers,
> because it can't be named? Can't even be called 'X'? Because otherwise
> we would add one to X and get a contradiction. Hmm, do I need to add a
> notion of "unnamable number" to my existing notion of "imponderable"?
> (I'll use this as shorthand for "imponderably enormous")
Yeah, and you can throw your "largest finite natural" in there too. You folks
seem to like numbers like that, so you might as well start a collection.
>
> Well, no, I don't. The whole point of considering an axiomatically
> defined (somewhat arbitrary) reference imponderable (your 'N') is that
> there can't be a clearcut threshold between ponderable and imponderable
> numbers.

Right. This is what we had referred to as the Twilight Zone between finite and
infinite, that uncountable chasm.

> Therefore, if we decide to consider the set of ponderably long
> strings, and get a value of 'F' for how many there are, then if someone
> produces the expression 'F+1' (for example), we of course can ponder
> it, since it's only one more than something else that's ponderable. Any
> incipient "contradiction" is due to the inappropriateness of tools that
> were designed for doing proper maths.
(sigh)
>
> Brian Chandler
> http://imaginatorium.org
>
>

--
Smiles,

Tony
.

Relevant Pages

  • Re: infinity
    ... <and wrote and wrote and wrote: snip> ... > I claim that there are a finite number of finite strings. ... we would add one to X and get a contradiction. ... produces the expression 'F+1', we of course can ponder ...
    (sci.math)
  • Re: infinity
    ... > aeo6 Tony Orlow wrote: ... > He's claiming that the sum of all the finite numbers is ... itself in its sum, which causes a contradiction. ... and ALL sets which just include finite strings are finite, ...
    (sci.math)
  • Re: infinity
    ... > aeo6 Tony Orlow wrote: ... >> infinite, and you cannot have an infinite language. ... There is no one L for all finite strings, but L for every string is finite, so ...
    (sci.math)
  • Re: infinity
    ... > aeo6 Tony Orlow wrote: ... >>> Daryl McCullough ... >> all lengths are finite, then none are infinite, and the language cannot be ... > that includes ALL FINITE STRINGS. ...
    (sci.math)
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