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Topic: mathematical infinite as a matter of method
Replies: 25   Last Post: May 4, 2013 11:24 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: mathematical infinite as a matter of method
Posted: May 3, 2013 7:19 PM

On May 3, 8:15 pm, fom <fomJ...@nyms.net> wrote:
> On 5/3/2013 2:43 AM, Graham Cooper wrote:
>
>
>

> > Its not possible to test Equality by Extension in the inf. case.
>
> That is correct Herc.
>
> On the other hand,  it is not possible to interpret
> the universal quantifier as a universal statement if
> it is interpreted as a course-of-values.

Humans do it.

How do you know:

nats /\ odds = odds ?

Somewhere in the calculations induction is going on...

element-n matches -> element-n+1 matches

>
> Aristotle wrote this.  It is ignored by a certain
> contingent of the mathematical community who merely
> argues on the basis of beliefs concerning infinity.
>
> You know well that any computer system balances
> choices that affect performance.  Relational databases
> run faster on logic chips optimized for integral
> arithmetic as opposed to floating point.  The analogy
> applies here.
>
> Brouwer had been clear concerning how the effectiveness
> of working with finite sets differed from working
> with infinite sets.  But, the reason infinity enters
> mathematics is because it is how the identity relation
> is extended to convey the geometric completeness of a
> line when used to represent the real number system.
>
> Infinity does not arise because of testability.  It
> arises because of the nature of the identity relation.
>

Well its fine to call it all philosophy anyway, but there
are real world problems here!

Most of ZFC axioms port across to PROLOG...

AXIOM OF PAIRING

e( A , union( S1, S2 ) ) :- e( A , S1 ).
e( A , union( S1, S2) ) :- e(A , S2 ).

Now you can WRITE EXPRESSIONS with UNION

eq( union( odds, evens) , nats ) ?
> YES

but the AXIOM OF EXTENSIONALITY

(set equality) is completely useless on infinite sets.

Herc

--
www.BLoCKPROLOG.com

Date Subject Author
4/21/13 fom
4/21/13 Virgil
5/2/13 Hercules ofZeus
5/2/13 fom
5/2/13 Virgil
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Brian Q. Hutchings
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper
5/3/13 fom
5/3/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/4/13 fom
5/4/13 Graham Cooper
5/3/13 Graham Cooper