|
|
Tony Orlow wrote:
> stephen@xxxxxxxxxx wrote:
> > Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
> >> stephen@xxxxxxxxxx wrote:
> >>> Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
> >>>> stephen@xxxxxxxxxx wrote:
> >>>>> Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
> >>>>>> stephen@xxxxxxxxxx wrote:
> >>>>> <snip>
> >>>>>
> >>>>>>> What does that have to do with the sets IN and OUT? IN and OUT are
> >>>>>>> the same set. You claimed I was losing the "formulaic relationship"
> >>>>>>> between the sets. So I still do not know what you meant by that
> >>>>>>> statement. Once again
> >>>>>>> IN = { n | -1/(2^(floor(n/10))) < 0 }
> >>>>>>> OUT = { n | -1/(2^n) < 0 }
> >>>>>>>
> >>>>>> I mean the formula relating the number In to the number OUT for any n.
> >>>>>> That is given by out(in) = in/10.
> >>>>> What number IN? There is one set named IN, and one set named OUT.
> >>>>> There is no number IN. I have no idea what you think out(in) is
> >>>>> supposed to be. OUT and IN are sets, not functions.
> >>>>>
> >>>> OH. So, sets don't have sizes which are numbers, at least at particular
> >>>> moments. I see....
> >>> If that is what you meant, then you should have said that.
> >>> And technically speaking, sets do not have sizes which are numbers,
> >>> unless by "size" you mean cardinality, and by "number" you include
> >>> transfinite cardinals.
> >
> >> So, cardinality is the only definition of set size which you will
> >> consider.....your loss.
> >
> > If somebody presents another definition of set size, I will
> > consider it. You have not presented such a definition.
> >
> >
>
> I have presented an approach that works for the majority of infinite
> bijections, and explained some of the exceptions. IFR works for all
> numeric sets mapped from a common set. N=S^L works for all languages,
> including those that express the first set. Both work on a parameteric
> basis, using infinite case induction to finely order the values of
> formulas for a specific infinite n. Rare exceptions include the set 1/n
> for neN, whose inverse is itself, which IFR ends up saying has size 1,
> but that's because the natural indexes and fractional mapped reals only
> share one point in their range, 1. So, I think Bigulosity is worth
> considering.
Why? What is it good for? What theories is it used in?
--
mike.
|
|