Virgil
Posts:
6,967
Registered:
1/6/11


Re: mathematical infinite as a matter of method
Posted:
May 2, 2013 10:21 PM


In article <749e1561d69b45af90013be3141ad4d7@ua8g2000pbb.googlegroups.com>, 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.kobeu.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. 

