Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: No Identity Bijection for Omega
Replies: 116   Last Post: Sep 22, 2007 5:58 PM

 Messages: [ Previous | Next ]
 George Greene Posts: 448 Registered: 12/12/04
Re: No Identity Bijection for Omega
Posted: Sep 12, 2007 10:51 AM

> On Sep 11, 11:04 am, MoeBlee <jazzm...@hotmail.com> wrote:
> > I'd give this in the
> > order in which the objects are defined:

> > A = w+1 = {0 1 2 ... w}
> > B = A\{0} = {1 2 3 ...w}
> > S = the successor function on w
> > F = Su{<w w>} = {<0 1> <1 2> ... <w w>}
> > X = A/\B = {1 2 3 ... w}

If X is the intersection of A and B then since B is a subset of A,
you have X=B. That needed to be stressed.

On Sep 11, 10:59 pm, logic...@comcast.net wrote:
> > > /now define a family of bijections, G():
>
> > > For each x in X replace {<x,b_n>, <a_m,x>}
> > > with {<x,x>, <a_m,b_n>}

>
> > That makes no sense to me. (1) Neither 'a' not 'b' have been defined.
> > (2) the members of X are not of the form of an unordered pair of
> > ordered pairs.

> a_m is a member of setA.

Therefore, a_m = m.

> b_n is a member of set B.

Therefore, arguably, b_n = n, unless you meant b_n = n+1.
It's got to be one or the other. But which? You (Russ) invite
confusion
by talking about b_0 when 0 is NOT a member of B.
But if you want b_0 to in fact be THE FIRST/SMALLEST element of B,
THEN YOU (Russ) need to SAY that, AND NOT say that b_n is *a* member
of B. You have to say WHICH member, in terms of n (which is trivially
simple,
so simple that even YOU could do it, if you mean it is the nth
member).

> The ordered pairs are members of F.
> x is a member of X and must also be
> a member of both A and B.
>
> Let x = w.

That is just barely coherent so far.

> Replace <w,w> and <w,w> in F
> with <w,w> and <w,w>.

That makes no sense. You can't have two copies of the same
thing in the same set. And replacing anything with ITSELF is just
doing NOTHING AT ALL.

> This is a new bijection
> (assuming F is a bijection).

No, it is NOT new; it is THE SAME OLD bijection because you have
only "replaced" things with THEMSELVES.

Date Subject Author
9/3/07 Russell Easterly
9/3/07 Chris Menzel
9/4/07 William Elliot
9/4/07 Russell Easterly
9/4/07 William Elliot
9/4/07 Patricia Shanahan
9/4/07 David C. Ullrich
9/4/07 Mitch
9/7/07 Russell Easterly
9/7/07 Patricia Shanahan
9/7/07 George Greene
9/7/07 Alan Smaill
9/12/07 George Greene
9/7/07 Jesse F. Hughes
9/8/07 tchow@lsa.umich.edu
9/12/07 George Greene
9/12/07 tchow@lsa.umich.edu
9/12/07 tchow@lsa.umich.edu
9/12/07 George Greene
9/7/07 lwalke3@lausd.net
9/7/07 George Greene
9/7/07 lwalke3@lausd.net
9/10/07 George Greene
9/11/07 lwalke3@lausd.net
9/11/07 George Greene
9/11/07 Jack Markan
9/11/07 George Greene
9/10/07 George Greene
9/7/07 George Greene
9/7/07 George Greene
9/7/07 Jack Markan
9/7/07 George Greene
9/7/07 Jack Markan
9/7/07 Jack Markan
9/8/07 Russell Easterly
9/8/07 Patricia Shanahan
9/8/07 lwalke3@lausd.net
9/8/07 Russell Easterly
9/8/07 Patricia Shanahan
9/8/07 Russell Easterly
9/8/07 Patricia Shanahan
9/9/07 Russell Easterly
9/9/07 Ross Finlayson
9/9/07 Patricia Shanahan
9/9/07 Russell Easterly
9/9/07 Patricia Shanahan
9/9/07 Jesse F. Hughes
9/9/07 Russell Easterly
9/9/07 Russell Easterly
9/10/07 Jesse F. Hughes
9/10/07 Patricia Shanahan
9/10/07 Russell Easterly
9/10/07 Patricia Shanahan
9/12/07 Russell Easterly
9/12/07 Jack Markan
9/10/07 Jack Markan
9/10/07 Russell Easterly
9/10/07 William Hughes
9/11/07 Russell Easterly
9/11/07 William Hughes
9/10/07 Jesse F. Hughes
9/11/07 Jack Markan
9/11/07 Russell Easterly
9/12/07 George Greene
9/12/07 Jack Markan
9/12/07 Russell Easterly
9/12/07 William Hughes
9/13/07 Russell Easterly
9/13/07 William Hughes
9/13/07 Russell Easterly
9/13/07 William Hughes
9/13/07 Jesse F. Hughes
9/13/07 Jack Markan
9/17/07 Jack Markan
9/17/07 Russell Easterly
9/17/07 William Hughes
9/18/07 Jesse F. Hughes
9/19/07 Russell Easterly
9/19/07 William Hughes
9/19/07 George Greene
9/19/07 Jesse F. Hughes
9/18/07 Jack Markan
9/20/07 Russell Easterly
9/20/07 William Hughes
9/20/07 Jesse F. Hughes
9/22/07 reasterly@gmail.com
9/13/07 George Greene
9/10/07 George Greene
9/10/07 Jack Markan
9/8/07 Jesse F. Hughes
9/8/07 Patricia Shanahan
9/8/07 William Hughes
9/10/07 Jack Markan
9/9/07 David R Tribble
9/4/07 George Greene
9/4/07 George Greene
9/4/07 William Hughes
9/4/07 Schroeder
9/4/07 Jack Markan
9/4/07 lwalke3@lausd.net
9/4/07 Jack Markan
9/4/07 G. Frege
9/5/07 Peter Webb
9/5/07 Jack Markan
9/5/07 Daryl McCullough
9/5/07 G. Frege
9/6/07 Jack Markan
9/7/07 hagman
9/7/07 lwalke3@lausd.net
9/7/07 Jack Markan
9/7/07 lwalke3@lausd.net
9/5/07 lwalke3@lausd.net
9/5/07 Jack Markan
9/5/07 herb z
9/5/07 Jack Markan
9/6/07 herb z
9/6/07 Jack Markan