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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 ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: mathematical infinite as a matter of method
Posted: May 2, 2013 10:21 PM

In article
Hercules ofZeus <herc.is.here@gmail.com> wrote:

> On Apr 21, 5:39 pm, Virgil <vir...@ligriv.com> wrote:
> > In article <Me6dnerBAcAL8O7MnZ2dnUVZ_rWdn...@giganews.com>,
> >
> >  fom <fomJ...@nyms.net> wrote:

> > > This is a easy, readable paper of the same
> > > title by Kanamori.  A historical analysis
> > > of how infinity entered mathematical discourse.

> >
> > >http://kurt.scitec.kobe-u.ac.jp/~fuchino/xpapers/infinity.pdf
> >
> > > OP: Marc Garcia at FOM
> >
> > > (Virgil -- you will find a familiar proof
> > > at the bottom of page 5)

> >
> > Yes! A nice version of it, too.
> >
> > And a nice paper which shows just how far out of any real mathematics WM
> > has put himself.
> >

>
> there is no _method_ to any of it though...
>
> DEFINE digit1 is different to row1, digit2 is different to row2, and
> so on...
> therefore infinite strings are bigger sets than finite strings...
>
> Its merely ONTO, SURJECTIVE definitions thrown directly onto
> a good optical effect of looking down the infinite plane at an angle
>
> no new digit sequence is EVER constructed using this 'method' and this
> is provable.

If you think it provable, then prove it to be provable by proving it.

Ontherwise, what you merely claim is no evidence.
>
> ----
>
>
> what would be useful is a procedural system with
>
>
> ..
>
> INTERSECTION
>
> in( S1, S2 ) <- E(X) XeS1 & XeS2
>
> ..
>
> SUBSET
>
> ss( S1, S2 ) <- ALL(X) XeS1 -> XeS2
>
> ..
>
> EQUALS
>
> eq( S1, S2 ) <- ss(S1, S2) & ss(S2, S1)
>
>
> --------------
>
> This checks both ways that all elements of S1 are elements of S2
> and vice versa!
>
>
> -------------
>
> Then some arithmetic can be added...
>
> nat(0)
> nat( s(X) ) <- nat(X)
>
> odd( s(0) )
> odd( s(s(X)) ) <- odd(X)
>
> even( 0 )
> even( s(s(X)) ) <- even(X)
>
> ---------------
>
> e.g.
>
> even(( s(s(s(s(0)))) ) ?
>

> > YES
>
> --------------
>
>
> Then sets can be defined using N.S.T.
>
> e( A, odds) <- odd( A )
> e( A, evens) <- even(A)
> e( A, nats ) <- nat( A )
>
> ---------------
>
> Now you can use the SET LEVEL OPERANDS.
>
> in( nats , odds ) ?
>

> > YES
>
> ....
>
> in( evens , odds ) ?
>

> > NO
>
> ...
>
> ss( odds , nats ) ?
>

> > YES
>
> ----------------------------

>
> EQUALITY BY EXTENSION
>
> fails on infinite sets.

But inequality by extention succeeds on sets which are no more than
countably infinite.

>
> What's needed is EQUALITY BY INDUCTION...
>
> before you can even HAVE an INFINITE SET THEORY
>
> that works!

While no doubt useful, such a requirement is not at all necessary.
--

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