On Wed, 16 May 2001 22:32:02 -0500, "Batronyx"
<bat### [at] cadronhsacom> wrote:


>I think I follow this. . . at the least the 2d version. Starting with a single
>small box and progressing first right and then down, repeat everything that came
>before and enclose in another box to express it as a set, right?

Yes.  The smallest box is the empty set i.e. zero.  Then you get the
set containing zero (one), then the set containing zero and one (two)
etc.  The traced version shows zero, then one next to it, then two
below them, then three behind all of those, four beside, five below,
six behind etc.  The complete figure has zero through nine, all
surrounded by a box to make ten. 
>
>Then just perform the process 10 times and finish with a single box to maintain
>consistent set notation.
>
>The 3 versions are harder to follow -- can't tell if you're going up,down left,
>right or what. The 2d version would make an interesting texture pattern. BTW I'm
>no math expert but I think this more like 'factorial' set notation.

IIRC, this is the von Neumann definition of the ordinal numbers.  I
read about this several years ago in a book by Rudy Rucker.  He had a
cartoon of a person thinking nested "thought balloons" to illustrate
the concept.  I remembered that and decided to play with the idea.

The code would be much cleaner and more efficient if I had used
recursion and/or a static lookup table.  For such a trivial thing cut
and paste coding seemed adequate.

BTW, I posted that from a place in which I prefer not to leave
personal info.  Hence the x@x.x.

Jerry Anning
cle### [at] dholorg

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