Re: Two results of set geometry

On Sep 26, 2:32 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 26 Sep., 20:03, William Hughes <wpihug...@xxxxxxxxxxx> wrote:


Appending one to each of the *elements* of the complete
column is not adding one to omega. Appending one to the
*set* of all elements, the complete column, is adding one to omega.
Appending 1 to the complete column produces a column
of length omega+1.

Every finite segment is the set of smaller finite segments.

No, every finite segment is a *set* of indices.
This set contains the index that corresponds to the finite
segment in question. (You are
confusing finite segments with ordinals, they are not quite
the same thing).

There is
no reason to distinguish the complete set from the others.

Correct. The complete set is the *set* of all the indices
(equivalently, the set of all the finite segments).
However, it is not a finite segment. Nor is the complete
set an element of the complete set.


Perhaps you> see now that your idea of a set is a chimera?

No. As WM has pointed out, every initial
(finite or not) segment is a *set*.

There is a bijection between the *elements* of the complete column,
and the *elements* of the set of rows.

- William Hughes

.

Relevant Pages

  • Re: Two results of set geometry
    ... Appending 1 to each finite segment is not ... infinite segment, even of order type omega + 1. ... indices to use, but if it is appended to a finite segment, it merey ... It is WM's idea of a set which is the chimera. ...
    (sci.math)
  • Re: Two results of set geometry
    ... By completed I mean a column of ordinal number omega. ... (larger than every finite segment of the column). ... the horizontal component, because this component is not infinite. ... potential infinity. ...
    (sci.math)
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