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Topic: Set Theory: Should you believe?
Replies: 778   Last Post: Aug 8, 2006 12:02 PM

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Rupert

Posts: 3,810
Registered: 12/6/04
Re: Set Theory: Should you believe?
Posted: Jul 20, 2006 5:59 AM
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Patricia Shanahan wrote:
> Lester Zick wrote:
> > On Fri, 14 Jul 2006 21:41:59 GMT, Stephen Montgomery-Smith
> > <stephen@math.missouri.edu> wrote:
> >

> >> Patricia Shanahan wrote:
> >>> Stephen Montgomery-Smith wrote:
> >>>

> >>>> guenther vonKnakspot wrote:
> >>>>

> >>>>> Stephen Montgomery-Smith wrote:
> >>>>
> >>>>

> >>>>>> Now, one of the respondents said that Norm had rejected the axiom of
> >>>>>> infinity, and so how is he supposed to do number theory. But
> >>>>>> nowhere in
> >>>>>> his article has he rejected the axiom of infinity. He has rejected the
> >>>>>> whole notion that axioms are the way to go. I would paraphrase what he
> >>>>>> said slightly differently - axioms (might) describe the natural
> >>>>>> numbers,
> >>>>>> but they don't define them. There is clearly a problem that there are
> >>>>>> numbers between 1 and googolplex that we can never write down or
> >>>>>> meaningfully describe. What makes us think that they are really there?
> >>>>>> The evidence is at best empirical.

> >>>>>
> >>>>> Think about your above paragraph for a minute. Do you really think that
> >>>>> the Number 2 is more real than some natural number which has never been
> >>>>> mentioned or even thought of? Do you really think that "2" is the
> >>>>> Number 2 ? "2" is the representation in one particular language of the
> >>>>> name in one particular language of the Number 2. The Number 2 is
> >>>>> neither its name in any language nor the representation of any such
> >>>>> name in any particular language. The Number 2 is something which does
> >>>>> not exist physically and can not be experienced by the senses. It is an
> >>>>> abstract concept as are all other numbers.

> >>>>
> >>>> I think your opening "think about it" sums it up best. The answer is
> >>>> not obvious to me. I do personally hold some Platonic belief that
> >>>> each of the natural numbers, even all of those between 1 and
> >>>> googolplex, have an abstract existence. But I regard my viewpoint as
> >>>> more a statement of faith (perhaps something that is quote self
> >>>> evident unquote) than anything else. I think that questioning my
> >>>> viewpoint is a reasonable thing to do and not at all crankish.

> >>>
> >>> Isn't there also a simplicity argument here? The set of all natural
> >>> numbers, with no gaps and no end, is in many ways an easier thing to
> >>> reason about than the set of natural numbers that someone, somewhere,
> >>> has used or will use.

> >> I have always regarded this kind of occum's razor type argument as a
> >> rule of thumb rather than a hard and fast method of deduction. But I
> >> think you make a good point - if we restrict ourselves to only saying
> >> that computable numbers exist, we leave a lot of very awkward gaps in
> >> the natural numbers. (I mean, how do you even properly define
> >> 'computable' - Cantor type diagonal arguments are always going to say
> >> any definition is incomplete, like 'the smallest number that cannot be
> >> described in less than 13 words.')

> >
> > If we're to take Turing at his word I suspect computable numbers are
> > nothing more than what can be produced using Turing mechanics.

>
> For every natural number n, there is a Turing machine that writes n "1"
> symbols to its output tape.
>
> "computability" in that sense only gets interesting for the real
> numbers, where there is a subset for which there is a TM that, given
> input k, can write the first k bits of its binary expansion, or equivalent.
>
> Note that NW must mean something different by "computability" because he
> says in http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf,
> "Think clearly about the subject for a few days, and you will see that
> the computable real numbers are not countable, and are complete."
>
> The set of all Turing machine computations (combination of a TM
> specification and input) is countable, so his definition of "computable"
> must include real numbers that are not the result of a TM computation.
>
> Patricia


No, he is using the standard definition of "computable number". When he
says they are not countable, what he means is that they are not
effectively countable.



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Read Re: Set Theory: Should you believe?
Chas Brown
7/19/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/19/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/20/06
Read Re: Set Theory: Should you believe?
Shmuel (Seymour J.) Metz
7/19/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/19/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/20/06
Read Re: Set Theory: Should you believe?
Shmuel (Seymour J.) Metz
7/20/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/20/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/20/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/20/06
Read Re: Set Theory: Should you believe?
David Bernier
7/21/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/21/06
Read Re: Set Theory: Should you believe?
George Greene
7/18/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/17/06
Read Re: Set Theory: Should you believe?
Russell Easterly
7/17/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/17/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/17/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/17/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/17/06
Read Re: Set Theory: Should you believe?
Patricia Shanahan
7/17/06
Read Re: Set Theory: Should you believe?
malbrain@yahoo.com
7/17/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/17/06
Read Re: Set Theory: Should you believe?
Virgil
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
Jan Burse
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/18/06
Read Re: Set Theory: Should you believe?
Rupert
7/18/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/19/06
Read Re: Set Theory: Should you believe?
Rupert
7/20/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/27/06
Read Re: Set Theory: Should you believe?
Rupert
7/27/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/28/06
Read Re: Set Theory: Should you believe?
Rupert
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Virgil
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Virgil
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/30/06
Read Re: Set Theory: Should you believe?
Virgil
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Rupert
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/29/06
Read Re: Set Theory: Should you believe?
Rupert
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Rupert
7/19/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Rupert
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/25/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/25/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/26/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/27/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/28/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/28/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/29/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/30/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
herbzet@cox.net
7/20/06
Read Re: Set Theory: Should you believe?
Rupert
7/21/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/21/06
Read Re: Set Theory: Should you believe?
Rupert
7/21/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/22/06
Read Re: Set Theory: Should you believe?
Rupert
7/23/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/24/06
Read Re: Set Theory: Should you believe?
Rupert
7/24/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/24/06
Read Re: Set Theory: Should you believe?
Rupert
7/27/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/27/06
Read Re: Set Theory: Should you believe?
Rupert
7/29/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/29/06
Read Re: Set Theory: Should you believe?
Rupert
7/30/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/31/06
Read Re: Set Theory: Should you believe?
namducnguyen
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/25/06
Read Re: Set Theory: Should you believe?
Rupert
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/23/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/25/06
Read Re: Set Theory: Should you believe?
Chris Menzel
7/25/06
Read Re: Set Theory: Should you believe?
Gc
7/26/06
Read Re: Set Theory: Should you believe?
Chris Menzel
7/26/06
Read Re: Set Theory: Should you believe?
Gc
7/28/06
Read Re: Set Theory: Should you believe?
George Greene
7/28/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
Pierre Asselin
7/25/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/26/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
Pierre Asselin
7/27/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/26/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/26/06
Read Re: Set Theory: Should you believe?
Gc
7/24/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/24/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/24/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/25/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/25/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/21/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/21/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/22/06
Read Re: Set Theory: Should you believe?
Patricia Shanahan
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/23/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/23/06
Read Re: Set Theory: Should you believe?
Virgil
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Virgil
7/18/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/18/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
David Bernier
7/19/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/22/06
Read Re: Set Theory: Should you believe?
Keith Ramsay
7/22/06
Read Re: Set Theory: Should you believe?
David Bernier
7/22/06
Read Re: Set Theory: Should you believe?
Virgil
8/3/06
Read Re: Set Theory: Should you believe?
Rupert
7/17/06
Read Re: Set Theory: Should you believe?
Toni Lassila
7/14/06
Read Re: Set Theory: Should you believe?
Phil Carmody
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/20/06
Read Re: Set Theory: Should you believe?
Y. T.
7/13/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Kevin Karn
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/15/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/15/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/15/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/15/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/15/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/15/06
Read Re: Set Theory: Should you believe?
Barb Knox
7/15/06
Read Re: Set Theory: Should you believe?
Daryl McCullough
7/15/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/15/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/15/06
Read Re: Set Theory: Should you believe?
T.H. Ray
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/17/06
Read Re: Set Theory: Should you believe?
James Dolan
7/14/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/17/06
Read Re: Set Theory: Should you believe?
Rupert
7/13/06
Read Re: Set Theory: Should you believe?
Russell Easterly
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
stephen@nomail.com
7/13/06
Read Re: Set Theory: Should you believe?
Virgil
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
lDontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
John Jones
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/13/06
Read Re: Set Theory: Should you believe?
Kevin Karn
7/13/06
Read Re: Set Theory: Should you believe?
Russell Easterly
7/13/06
Read Re: Set Theory: Should you believe?
Kevin Karn
8/4/06
Read Re: Set Theory: Should you believe?
seand602
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/13/06
Read Re: Set Theory: Should you believe?
lDontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Aatu Koskensilta
7/14/06
Read Re: Set Theory: Should you believe?
Shmuel (Seymour J.) Metz
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/16/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/14/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/14/06
Read Re: Set Theory: Should you believe?
Soap_Dude
7/16/06
Read Re: Set Theory: Should you believe?
R. Srinivasan
7/16/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/17/06
Read Re: Set Theory: Should you believe?
Rupert
7/13/06
Read Re: Set Theory: Should you believe?
Daryl McCullough
7/13/06
Read Re: Set Theory: Should you believe?
tez_h@nospam.yahoo.com
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/15/06
Read Re: Set Theory: Should you believe?
George Greene
7/15/06
Read Re: Set Theory: Should you believe?
David Petry
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/15/06
Read Re: Set Theory: Should you believe?
Andrew Bettilyon
7/16/06
Read Re: Set Theory: Should you believe?
George Greene
7/17/06
Read Re: Set Theory: Should you believe?
Andrew Bettilyon
7/16/06
Read Re: Set Theory: Should you believe?
bogus address
7/16/06
Read Alternative Trigonometry: [Was: Re: Set Theory: Should you believe?]
Patricia Shanahan
7/16/06
Read Re: Alternative Trigonometry: [Was: Re: Set Theory: Should you believe?]
Patricia Shanahan
7/17/06
Read Re: Alternative Trigonometry: [Was: Re: Set Theory: Should you believe?]
Andrew Bettilyon
7/13/06
Read Re: Set Theory: Should you believe?
George Greene
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Ralf Bader
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/15/06
Read Re: Set Theory: Should you believe?
Virgil
7/15/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/16/06
Read Re: Set Theory: Should you believe?
Virgil
7/16/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/18/06
Read Re: Set Theory: Should you believe?
Rupert
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/19/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/19/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/20/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/20/06
Read Re: Set Theory: Should you believe?
Virgil
7/20/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/24/06
Read Re: Set Theory: Should you believe?
Rupert
7/24/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
Rupert
7/14/06
Read Re: Set Theory: Should NW behave?
George Greene
7/14/06
Read Re: Set Theory: Should you believe?
T.H. Ray
7/12/06
Read Re: Set Theory: Should you believe?
Gonçalo Rodrigues
7/12/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/12/06
Read Re: Set Theory: Should you believe?
David Petry
7/12/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Richard Herring
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gerry Myerson
7/14/06
Read Re: Set Theory: Should you believe?
Lee Rudolph
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
kunzmilan@atlas.cz
7/13/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
Dr. David Kirkby
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
David C. Ullrich
7/14/06
Read Re: Set Theory: Should you believe?
David C. Ullrich
7/14/06
Read Re: Set Theory: Should you believe?
Peter Webb
7/14/06
Read Re: Set Theory: Should you believe?
jirka@5z.com
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/13/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/14/06
Read Re: Set Theory: Should you believe?
David C. Ullrich
7/13/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/13/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/13/06
Read Re: Set Theory: Should you believe?
Brian Chandler
7/13/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/13/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/14/06
Read Re: Set Theory: Should you believe?
Ben Rudiak-Gould
7/14/06
Read Re: Set Theory: Should you believe?
guenther.vonKnakspott@gmx.de
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
stephen@nomail.com
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Gene Ward Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
Dave L. Renfro
7/14/06
Read Re: Set Theory: Should you believe?
DontBother@nowhere.net
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Stephen Montgomery-Smith
7/14/06
Read Re: Set Theory: Should you believe?
Chas Brown
7/13/06
Read Re: Set Theory: Should you believe?
Hatto von Aquitanien
8/3/06
Read Re: Set Theory: Should you believe?
Anonymous

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