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Topic: Eliminating Quantifiers For Dummies! A(x) E(y) ALL(t)EXIST(u)EaAb ..
Replies: 50   Last Post: Jan 28, 2012 11:25 AM

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 Tony Bones Orlow Posts: 164 Registered: 8/17/11
Re: Eliminating Quantifiers For Dummies! A(x) E(y) ALL(t)EXIST(u)EaAb ..
Posted: Jan 26, 2012 5:46 PM

On Jan 26, 1:10 pm, Frederick Williams <freddywilli...@btinternet.com>
wrote:
> Tony Orlow wrote:
>

> > On Jan 26, 9:43 am, Frederick Williams <freddywilli...@btinternet.com>
> > wrote:

>
> > > Can all sets be got by starting with the null set and singletons; adding
> > > single elements; and taking unions of two sets?

>
> > Actually, many are gotten by defining xeS <-> P(x), but that makes the
> > whole discussion rather trivial, wouldn't you say? The set union
> > statements are meant to cover combinations of sets over which P(x) is
> > true. What's your point, exactly?

>
> My point was that starting with the null set and singletons, adding
> single elements, and taking unions of two sets gets you very little.  It
> will not allow you to show that
>
>    {0, 1, 2, 3, ...}
>
> is a set, for example.
>
> --
> When a true genius appears in the world, you may know him by
> this sign, that the dunces are all in confederacy against him.
> Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

So? You throw in the axiom of infinity, if that's the set you want to
talk about. It's defined piecemeal anyway, element-wise and
recursively. What I am talking about is quantification over a base
set.

Peace,

Tony

Date Subject Author
1/23/12 Alan Smaill
1/23/12 Dan Christensen
1/23/12 Dan Christensen
1/24/12 Frederick Williams
1/24/12 Dan Christensen
1/24/12 Rotwang
1/24/12 Dan Christensen
1/25/12 Rotwang
1/25/12 Ki Song
1/25/12 Dan Christensen
1/25/12 Rotwang
1/26/12 Dan Christensen
1/26/12 Tony Bones Orlow
1/26/12 Frederick Williams
1/26/12 Tony Bones Orlow
1/26/12 Frederick Williams
1/26/12 Tony Bones Orlow
1/26/12 William Hale
1/26/12 Tony Bones Orlow
1/26/12 William Hale
1/26/12 Tony Bones Orlow
1/26/12 MoeBlee
1/26/12 Dan Christensen
1/26/12 MoeBlee
1/26/12 Dan Christensen
1/26/12 MoeBlee
1/26/12 Dan Christensen
1/27/12 MoeBlee
1/26/12 Tony Bones Orlow
1/26/12 Dan Christensen
1/27/12 Tony Bones Orlow
1/27/12 Dan Christensen
1/27/12 Tony Bones Orlow
1/27/12 Frederick Williams
1/27/12 MoeBlee
1/27/12 Tony Bones Orlow
1/27/12 Tony Bones Orlow
1/27/12 MoeBlee
1/27/12 MoeBlee
1/27/12 MoeBlee