🚀 go-pugleaf

On Feb 23, 4:14 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 23, 8:11 pm, Zuhair <zaljo...@gmail.com> wrote:
>
>
>
>
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> > On Feb 23, 3:16 am, Chris Menzel <cmen...@remove-this.tamu.edu> wrote:
>
> > > On Tue, 21 Feb 2012 07:48:03 -0500, Shmuel Metz
> > > <spamt...@library.lspace.org.invalid> said:
>
> > > > While I find (a,b)={{a},{a,b}} to be more natural for ordered pairs,
> > > > it does not generalize well to m-tuples.
>
> > > But only in regard to "naturalness", right?  I mean, in general, for
> > > n>1, we have <a1,...,an,an+1> = <<a1,...,an>,an+1> = {{<a1,...,an>},
> > > {<a1,...,an>},{an+1}}, which is perfectly well defined under K's
> > > definition.
>
> > Ok Chris examine this definition of pairs which can generalize to n-
> > tuples
> > in a nice manner so that one can compare and see
>
> > Def.)  (a,b)= { {1,{a}} , {2,{b}} }
>
> > where 1 and 2 are the {{}} and {{},{{}}}  as in standard notation.
>
> > Now you can call this pair  Hausdorff's - Zuhair pair.
>
> > It is definitely less natural than Hausdorff's { {1,a} , {2,b} }
> > which is the most natural of all possible pairs because
> > it uses tagging with 1 and 2 to determine the order of
> > projections by simply pairing them in unordered manner
> > which is the most natural one, although this naturalness comes
> > at a high expense of complexity of defining projections.
>
> > Now my modification both ease the definition of projections
> > of that pair and not only that it is more powerful in the sense
> > of making it extending to any n-tuple for any ordinal n whether
> > finite or not!!! and this extension happens in a very natural manner!
>
> > so for example (a,b,c)= { {1,{a}} , {2,{b}} , {3,{c}} }
>
> > You see extending the pair here follows the same strategy
> > so (a,b,c,d,e)={ {1,{a}} , {2,{b}} , {3,{c}} , {4,{d}} , {5,{e}} }
>
> > This is much nicer and more elegant the Kuratowski nesting
> > and even more elegant than n-tuples defined as sequences
> > of length n depending on Kuratowski based ordered pairs.
>
> > Actually this method allows simpler definition of sequences
> > also, so instead of defining a sequence S of elements of set A
> > of length n as: S:N-->A, where S is a collection of Kuratowski
> > ordered pairs, one can similar define S:N--> P_1(A) where
> > S is a collection {n,{a}} pairs where neN and a e A.
>
> > Cheers
>
> > Zuhair
>
> None of these work!

OF course they work, why you think I wrote them?
>
> You are confusing  { (1, a), (2, b), (3, c) }  with  { {1, a},  {2,
> b}, {3, c} }

No I am not, you are simply BLIND  read well what I wrote
I didn't wright { {1,a} , {2,b} , {3,c} } as you said
I wrote { {1,{a}} , {2,{b}} , {3,{c}} } which is different
It seems that you don't know the difference between
{1,a} and {1,{a}}. My version works I am sure of that
I already have tested it, it works nicely as a tuple, it is
stratified and it can be generalized to any length n,
it is simple and admites the simples projection definition
among all n-tuples for a general n. You only missed the point.
Read well before responding!

>
> What is the order here?
>
> { {4, 1}, {1, 2}, {2, 3}, {3, 4} }
>
> <2 3 4 1> or <4 1 2 3> ?
>
> ***********************************************************
>
> You have to nest the braces outside of the ordered pair.
>
>  {   {a,{}} ,   {{b,{}}} ,   {{{c,{}}}} ,   {{{{d,{}}}}}   }
>
> Now (a, a) = { {a,{}}, {{a,{}}} }
>
> has 2 full elements, no singleton!
>
> since my design is based on your idea, how about Herc-Zuhair Set
> Ordering?
>
> Herc- Hide quoted text -
>
> - Show quoted text -