Re: Cantor Confusion

In article <1167492220.138771.111750@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

cbrown@xxxxxxxxxxxxxxxxx schrieb:

Have you given up on your "rational relation" proof that |N| = |R|?

No, why should I? It is correct. (A series with a first but no last
term can be reversed to have a last but no first term - without oosing
its value.)

How does one "sum" a series with no first term? There is no place to
start!

But it is easier to see, and should be visible even for such as you,
that the tree built from the union of all finite trees (with
representations of rational paths) is the same as the complete infinite
tree.

In the union of all finite trees, there are no infinite paths at all,
since to be represented in the union, a path would have to be in one of
the finite trees, ergo a finite path.

In the same way, the union of any family of sets of finite naturals does
not contain anything but finite naturals.
.

Relevant Pages

  • Re: Cantor Confusion
    ... >>> Therefore there is no uncuntable set of path in the union tree. ... > 2) The union tree Tof all finite trees is well defined (as I have ... are infinite paths in the union tree T. ...
    (sci.math)
  • Re: Review of Mueckenheims book.
    ... There is no definition in set theory that states: ... as as a set of naturals by taking the union which gives? ... > supplies that it cannot be larger than all nodes of the union. ... The union of all those finite trees is N. The edges are defined as ...
    (sci.math)
  • Re: Cantor Confusion
    ... In the union of all finite trees, there are no infinite paths at all, ... the union of any family of sets of finite naturals does ...
    (sci.math)
  • Re: Cantor Confusion
    ... finite trees contains infinite paths. ... Here is the formal proof: ... as union of initial seqments of the real number 0.111.... ...
    (sci.math)
  • Re: Cantor Confusion
    ... > of two finite trees is the set of paths of the larger tree. ... In the union of the sets of paths there are both paths that go ... of diagonals of the finite squares. ... The union of finite trees contains all sequences. ...
    (sci.math)