🚀 go-pugleaf

On Feb 23, 10:45 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 24, 1:30 am, Zuhair <zaljo...@gmail.com> wrote:
>
>
>
> > > 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
>
> <UNSNIP>
> Define <a,b>={{1,a},{2,b}}

Oh man, you are really confused I was speaking about the case of the
triple.

Let me make it clear for you:

For the ordered pair (n-tuple with n=2) yes we can define it as

<a,b>={ {1,a}, {2,b} }  with 1,2 being any two ordinals but it
is better to fix them as 1={0} and 2={0,1} as uaual.

so <a,b>={{{0},a} , { {0,{0}} , b}}

I already clarified that this cannot be extended in a natural
manner to n greater than 3

so you CANNOT have an ordered triple <a,b,c>={ {1,a} , {2,b} , {3,c} }

That's why I made a MODIFICATION on the original definition of
Hausdorff and this was

<a,b>= {{1,{a}} , {2,{b}}}   Now this pair is *DIFFERENT* from the
above one
because in set theory {a} is not always equal to a for all values of
a.

A clear example let a be the empty set i.e. a={ } , i.e. a is the set
that has not elements
Now {a} will be {{}} which is not empty so by Extensionality {a} is
different from a.
The case of "DUMMY" and {DUMMY} largely depends on what set you assign
to
the variable DUMMY if  DUMMY is a singleton set that is in itself then
of course
DUMMY={DUMMY}, but it not then it is not the case that DUMMY={DUMMY}
You need to understand this point in set theory.

So for the general a (i.e. *any* a)  {1,{a}} is not necessarily the
same as {1,a}.

Now this modified definition of mine i.e. <a,b>={{1,{a}} , {2,{b}}}
CAN be
extended infinitely in a natural manner to even an infinite extent.

Lets start with the finite ones:

<a,b,c> = { {1,{a}} , {2,{b}} , {3,{c}} }  where 1,2,3 are the usual
Von Neumann ordinals.

<a,b,c,d> = { {1,{a}} , {2,{b}} , {3,{c}} , {4,{d}} }

<a,b,c,d,e> = { {1,{a}} , {2,{b}} , {3,{c}} , {4,{d}} , {5,{e}} }

and so on, now those are ORDERED  n-tuples  for n=3,4,5 respectively

and in general we write: for any ordinal n

<a_1, a_2,..., a_n> = { {1,{a_1}} , {2, {a_2}} , {3, {a_3}} ,.....,
{n, {a_n}} }

Those do work!

Zuhair





> > I wrote { {1,{a}} , {2,{b}} , {3,{c}} } which is different
>
> Same bullshit.
>
> > It seems that you don't know the difference between
> > {1,a} and {1,{a}}. My version works I am sure of that
>
> a = dummy
> a = {dummy}
>
> Same dummy!
>
> > 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!
>
> I'm not going to correct you with the same correction a 4th time.
>
> > > What is the order here?
>
> > > { {4, 1}, {1, 2}, {2, 3}, {3, 4} }
>
> If you bothered to answer the question you would see your error.
>
>
>
> > > <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!
>
> Herc
> --http://Matheology.com