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la djorden cusku di'e
On Thu, Nov 21, 2002 at 12:54:23PM +0000, Jorge Llambias wrote:
> la djorden cusku di'e
> > > {so'a} and {so'e} are clearly relative to {ro}, unless
> > > the keywords ("almost all", "most") are totally meaningless.
> > > It seems to me that they are necessarily less than ro, and
> > > also at least ro/2.
> >
> >As was being discussed on the wiki, this sort of way of looking at
> >things has issues for infinite sets. ro/2 can be ro in those cases.
>
> But then "almost all" and "most" will also be infinite.
Right, but they shouldn't be the same as "all" (or at least, in
english they aren't.
In the same sense, ro/2 should not be the same as "all" either.
I can't say "All numbers are divisible by 2"). So we can't consider them to be a fraction of ro, I don't think, and we also can't consider "ro" to just be a cardinality indicator when used as an outer quantifier.
I really don't understand the point here.
> >I'd suggest viewing so'a and so'e as iterators along with ro. So, > >while ro executes your propositional function for every x, so'a and > >so'e execute for every x, but it should evaluate true for only every > >N x's, and false for the rest. > > I suspect you meant to say something else there. so'a/so'e > should evaluate true for an infinite number of cases when ro > is infinite, so it can't be true for only a finite number of > cases. Right; and they also evaluate false for an infinite number of cases.
Not necessarily. For example, we could say "almost all positive integers are greater than 10", which will evaluate to false for only a finite number of integers.
> You can't say either that for any finite subset it should evaluate
> as true for most of its members because for some selected
> subsets it will evaluate true for all members, for other
> selected subsets it will evaluate true for no members, etc.
I wasn't refering to a finite subset, just to the way the iteration
would work over the entire set. If I say {so'e namcu cu pilji lo
mulna'u li re}, I'm not really talking about how many namcu there
are which are pilji, but rather how many there are against the
background of numbers which aren't. So if we were to arrange the
elements in a particular order (in this case numerical order), and
then iterate over them, my function "it pilji lo mulna'u li re"
will be true every other time. (and there's an infinite number of
times).
I think this way of doing things can apply to ce'i actually without
requiring at least 100 elements. pace'i would mean that there is
an arrangement of the elements so that as you iterate over them you
hit 10 trues and then 90 falses, or any equivalent ratio. So if
there's only 10 elements, the arrangement where 1 is true and then
9 false will work.
I don't think anyone has any doubts about what {panoce'i} means
when the total number is finite, except perhaps that we don't know
whether it is to be taken as individuals or as a mass.
In the case of infinite sets, different orderings will give
different results. For example, if you order the integers like
this: 1, 10, 2, 20, 3, 30, 4, 40, 5, 50, 6, 60, 7, 70, 8, 80,
9, 90, 11, 110, 12, 120, ... you may be tempted to say that 50%
of the integers are multiples of 10. It will work using your
method. In fact any statement about fractions of infinity are
meaningless if taken strictly, but they have some non-explicit
meaning in the sense you propose plus some assumptions of
"standard ordering".
> >[...]
> > > >3. CAhA, da'i, mu'ei etc.
> > >
> > > ka'e = su'omu'ei
> > > ca'a = <this>mu'ei
> > > nu'o = ka'e jenai ca'a
> > > pu'i = ?
> >
> >not {ka'e je ca'a}?
>
> With the above definition, that reduces to {ca'a}.
Actually with the way you give ka'e and ca'a, anything which ca'a
must also ka'e.
Yes, undoubtedly.
So I don't see the problem. pu'i would just be another way to say it (but you could've just said ca'a).
I don't see a problem either, we'd just have two cmavo with
identical meaning. I never use {pu'i} as it is anyway.
I think the concept of "demonstrating" potential ("can and has")
really is about what has happened in the past.
These are probably a bit better though:
nu'o = pu ca'a naje ka'e
pu'i = pu ca'a je ka'e
That's how I've always interpreted it, but there has
been a certain reluctance to accept this officially.
Do you see any difference between {pu ca'a je ka'e}
and plain {pu ca'a}?
mu'o mi'e xorxes
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