BPFK Section: Inexact Numbers
wrote:
>
> pc:
> > --- Jorge LlambÃas wrote:
> > > This is what
> > > CLL says:
> > >
> > > Each of these numbers, plus ro, may be
> > > prefixed with pi (the decimal
> > > point) in order to make a fractional form
> which
> > > represents part of a whole
> > > rather than some elements of a totality.
> > > piro therefore means ''the whole
> > > of'':
> > >
> > >
> > > 8.8) mi citka piro lei nanba
> > > I eat the-whole-of the-mass-of bread
> > >
> > > Similarly, piso'a means ''almost the
> whole
> > > of''; and so on down to
> > > piso'u, a tiny part of. These
> numbers
> > > are particularly appropriate with
> > > masses, which are usually measured rather
> than
> > > counted, as Example 8.8 shows.
> >
> > I know that CLL says that {piPA lo broda} is
> 0.PA
> > of one broda.
>
> Can you indicate where? All I could find about
> fractional
> quantifiers in CLL is what I quoted above.
Top of page 131, lines 4-5. I don't place much
weight on it, of course.
> > It is also at variance
> > with what was (I thought) agreed on here
> earlier
> > (much earlier, to be sure) ion response to
> the
> > rather thorough muddle about quantified sumti
> in
> > CLL, that fractionals gave fractions of the
> total
> > size, not fractions of the members: external
> PA
> > was to understood, then, as PA/ro.
>
> I understand external PA as {PA fi'u ro}, i.e.
> PA out
> of all the referents of the sumti.
But, but, but ... if they are fractional, why are
the other fractions not fractional? I gather
that you want to distinguish between {pimu}, {pa
fi'u re} (and {mu fi'u pano}) and probably
{nopimu}. this is legitimate, but does seem to
need an explanation, since these are normally the
same.
>
> > I expect that we want to talk about half a
> group
> > of (or several) broda far more often than
> about
> > half a broda.
>
> I expect so too. Both are easy to do with the
> proposed
> system.
>
> > The standard way to say half a
> > broda otherwise is not much more complex that
> > {pimu lo broda}, while, lacking this form,
> saying
> > "half of the broda" seems rather harder --
> > certainly more so that its usefulnness
> suggests.
>
> {fi'u re lo broda}
>
> This form also has the advantage that "a third
> of the broda"
> is {fi'u ci lo broda} rather than the somewhat
> stranger
> {pira'eci lo broda}, not to mention {fi'u ze}
> for
> "a seventh" instead of {pira'epavorebimuze}.
>
> And there's also {muno ce'i lo broda}.
Yes, of course most decimal expansions are
messier than fractions, so we would generally use
fractions for them, but not when the decimal
expansion is shorter or maybe as short (I wonder
if shorter actually happens). By parity of
practical reasoning, if we want some sloppy
decimal of an object surely we would use the
fraction rather than the decimal there as well.
Of course, since this is very uncommon, we can
get by with long decimals in these cases. On the
other hand, the suggested {(fraction) se'i} would
always work and leave the simpler forms for the
more common cases (basically the same argument as
was made against using {PA1 lo PA2 broda} for PA1
examples of (groups of) PA2 objects. I find it
pretty convincing, all things considered.