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Re: Why not Hausdorff's ordered pairs
Posted:
Feb 23, 2012 2:49 PM
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On Feb 24, 5:44 am, Herman Rubin <hru...@skew.stat.purdue.edu> wrote:
> On 2012-02-23, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > What about:
> > { {a,{a}} , {{b,{b}}} , {{{c,{c}}}} , {{{{d,{d}}}} }
> > The level of redundancy in the duplicate braces represents the
> > position in the sequence.
> > Herc
> > --
> >http://Matheology.com
>
> There are models of set theory consistent with the usual
> ones in which for some sets u, u={u}. It will not work
> in such models.
>
Why not? The 2 member set is preserved as is the n-level nesting of
redundant braces to indicate position.
The improved version certainly works regardless of the values.
{ {a,{}} , {{b,{}}} , {{{c,{}}}} , {{{{d,{}}}}} }
Now (a, a) = { {a,{}}, {{a,{}}} }
has 2 members - no singleton!
Herc
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