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Topic: On Generalizing the Natural Numbers
Replies: 4   Last Post: Nov 25, 2012 10:04 PM

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Graham Cooper

Posts: 4,247
Registered: 5/20/10
Re: On Generalizing the Natural Numbers
Posted: Nov 25, 2012 9:43 PM
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On Nov 26, 11:01 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Nov 26, 3:37 am, George Greene <gree...@email.unc.edu> wrote:
> > On Nov 24, 6:59 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > Define ADD(a,b,c) as a+b=c
>
> > > For any relation P(,) defind P(I,x) as the
> > > process of inputting a value for I and outputting all values for x
> > > that are in that relation, where I in general is any number of
> > > components with values I, J, K, . .. and x is x, y, z, ...  That is,
> > > R(I,x) = { x | R(I,x) is true.}


...

>
> I think  pred(X, a, b, c)   <=>  { X | pred(X, a, b, c) }
>
> might be a more natural convention, X is argument 1.
>



There seems to be scope for a PREDICATE CALCULUS II
with {set notation} instead of using e(X,Y).

This reminds me of an article about development of the XML REQUEST
object that I was reading..

http://en.wikipedia.org/wiki/XMLHttpRequest
The World Wide Web Consortium published a Working Draft specification
for the XMLHttpRequest object on April 5, 2006, edited by Anne van
Kesteren of Opera Software and Dean Jackson of W3C.[17]

Its goal is "to document a minimum set of interoperable features based
on existing implementations, allowing Web developers to use these
features without platform-specific code."

------------------

It could be worth setting up a LOGIC CONSORTIUM of our own to define
the notation standard of PC2

I should be able to extend PROLOG to run Queries in this form..

all( X , less(X,10) , add( X, {2,3,4}, 20) )

^ ^ DOMAIN SUPERSET
| |
| TERM
|
QUANTIFIER


this is not yet compatible with Charlie's Method!

Herc




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