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Topic: SET THEORY and QUANTIFIER LOGIC are SUPERFLUOUS! You only need
1 or the other!

Replies: 8   Last Post: Nov 22, 2012 4:20 PM

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Charlie-Boo

Posts: 1,585
Registered: 2/27/06
Re: SET THEORY and QUANTIFIER LOGIC are SUPERFLUOUS! You only need 1
or the other!

Posted: Nov 20, 2012 10:59 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Nov 20, 4:09 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> The notation in
>
> { x | p(x) }
>
> stands for ALL VALUES OF x
> that are satisfied in p(x)
>
> This is the SAME 'ALL' as   ALL(x) ....predicate(..predicate...
> x  ...) ...)
>
> ALL is merely SUBSET!
>
> ALL(n):N  n+1 > n
>
> is just
>
> { n | neN }  C  { n | n+1>n }
>
> ----------------------
>
> ALL(x):N  xeR
>
> is just
>
> { x | xeN }  C  { x | xeR }
>
> Naturals are a subset of Reals!
>
> All Naturals are elements of Reals!
> A(x):N  xeR
>
> --------------------
>
> This is good news for me since I'm adding breadth first functionality
> to microPROLOG (sets of results) so I just have to figure out a set
> notation with { }.
>
> e.g.
> union( { 1 2 3 } , { 3 4 } , X }
>
> X = { 1 2 3 4 }
>
> So I can avoid the horrors of eliminating quantifiers by making you
> write the theorems in set theory notation instead!  Haha!
>
> Herc
>
> --www.microPROLOG.com
> if( if(t(S),f(R)) , if(t(R),f(S)) ).
>     if it's sunny then it's not raining
> ergo
>        if it's raining then it's not sunny


That's exactly right. No matther what people say to downplay your
ideas, the fact remains that we have two separate but parallel
branches of Mathematics viz. Set Theory and Logic.

I mentioned this a few years ago and of course the conservative
professors here ridiculed it as being stupid. Then someone pointed
out that there is a group of Mathematicians (read: professors) who are
working on combing Set Theory and Logic, and the criticism abruptly
stopped. My final comment: "Are those professors also stupid, or are
your criticisms simply blind allegiance to anyone who teaches and
ridicule of those who don't, with no mathematical significance?"

Also, Geometry = Algebra AFAIK. Lines, circles and other geometic
shapes are just equations. Intersections are solutions to
simultaneous equations.

When you really understand principles, you discover that many terms
are equivalent.

C-B



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