Ian Kelly wrote:
>Come to think of it, it's also more correct. A voting index of
>aleph-null should properly only be used when infinitely many FOR votes
>are placed,
Not at all. The voting index is not inherently a cardinal. It is
not a count of FOR votes, but (mostly) a ratio between two cardi
On 1/11/07, Zefram <[EMAIL PROTECTED]> wrote:
Ian Kelly wrote:
>Come to think of it, it's also more correct. A voting index of
>aleph-null should properly only be used when infinitely many FOR votes
>are placed,
Not at all. The voting index is not inherently a cardinal. It is
not a count of F
On 1/11/07, Zefram wrote:
(Imagine if it were possibleto cast a half vote.)
I've always thought this was a good idea... now if only i can come up with a
plausible way to implement it.
Ian Kelly wrote:
> By your argument, aleph-null should
>never be used for voting index, since aleph-null is not a hyperreal
>(as far as I am aware -- my understanding is that an infinite
>hyperreal is defined as the inverse of an infinitesimal hyperreal,
>which is
On 1/11/07, Zefram <[EMAIL PROTECTED]> wrote:
Ian Kelly wrote:
> By your argument, aleph-null should
>never be used for voting index, since aleph-null is not a hyperreal
>(as far as I am aware -- my understanding is that an infinite
>hyperreal is defined as the i
Ian Kelly wrote:
> And I'm not convinced that n/0 (I don't know whether
>it has a name, let's call it h)is actually a hyperreal,
It's not. It's undefined. That's why the Rule determining the voting
index needs a special case for where there are no AGAINST votes. 0/0 is
also unde
Zefram wrote:
Strictly, what we want for the case of zero AGAINST votes and more than
zero FOR votes is the limit of 1/n as n approaches zero from above.
I think that's aleph-0, but I'm not 100% sure. This does seem to match
your definition of an infinite hyperreal.
Applying the same logic to
Michael Norrish wrote:
>Life would be a lot simpler if we dispensed with ratios entirely, and
>framed AIs in terms of differences.
Interesting. I have a concept for quorum which might interact with
that idea. There is a problem with the usual way quorum works, that
there are situations where vo
On 1/11/07, Zefram <[EMAIL PROTECTED]> wrote:
Strictly, what we want for the case of zero AGAINST votes and more than
zero FOR votes is the limit of 1/n as n approaches zero from above.
I think that's aleph-0, but I'm not 100% sure. This does seem to match
your definition of an infinite hyperrea
On 1/11/07, Kerim Aydin <[EMAIL PROTECTED]> wrote:
I tried once, but according to Kelly I only said I did.
Mine.
--
C. Maud Image (Michael Slone)
I tried once, but according to Kelly I only said I did.
-- Goethe, in agora-discussion
P.S. She was right.
On 1/11/07, Michael Slone <[EMAIL PROTECTED]> wrote:
The rule we choose is the following. First select a nonprincipal
ultrafilter on the natural numbers.
I *hate* the ultrapower construction, because nobody's been able to
actually construct a free ultrafilter.
--
Taral <[EMAIL PROTECTED]>
"Yo
On 1/11/07, Taral <[EMAIL PROTECTED]> wrote:
I *hate* the ultrapower construction, because nobody's been able to
actually construct a free ultrafilter.
Nobody's been able to construct a free ultrafilter because it's
impossible to do so.
Hope this helps.
--
Michael Slone
On 1/12/07, Michael Slone <[EMAIL PROTECTED]> wrote:
On 1/11/07, Taral <[EMAIL PROTECTED]> wrote:
> I *hate* the ultrapower construction, because nobody's been able to
> actually construct a free ultrafilter.
Nobody's been able to construct a free ultrafilter because it's
impossible to do so.
H
On 1/12/07, Taral <[EMAIL PROTECTED]> wrote:
Yes, I know. Hence why I prefer the polynomial ratio construction.
Are you talking about the Schmieden--Laugwitz construction (using a cofinite
filter)? Their construction produces a ring with zero divisors, and
it isn't even
an ordered ring.
--
Mi
On 1/12/07, Michael Slone <[EMAIL PROTECTED]> wrote:
Are you talking about the Schmieden--Laugwitz construction (using a cofinite
filter)? Their construction produces a ring with zero divisors, and
it isn't even an ordered ring.
Hm, it seems I was mistaken.
--
Taral <[EMAIL PROTECTED]>
"You c
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