• From: Peter Hunsberger <peter.hunsberger@g...>
• To: Hermann Stamm-Wilbrandt <STAMMW@d...>
• Date: Thu, 9 Sep 2010 08:28:01 -0500

On Thu, Sep 9, 2010 at 5:56 AM, Hermann Stamm-Wilbrandt
<STAMMW@d...> wrote:
>
>> I guess Excel spreadsheets are three-dimensional - row, column, and
>> sheet number.
>
> All fixed dimension representations are countable.
> That means that each tuple can be mapped to a single number
> like this for 2 dimensions.
>
> .!.1..2..3..4 ...
> -----------------
> 1!.1..2..6..7 ...
> 2!.3..5..8 ...
> 3!.4..9.13 ...
> 4!10.12 ...
> 5!11 ...
> .
> .
> .
>
> So in effect fixed dimension tuples are 1-dimensional ...
>

No, the property you are referring to is cardinality. You have
demonstrated that fixed dimension tuples have the same cardinality
(Aleph null, in this case) as integer numbers. Cardinality is an
orthogonal concern to dimensionality (mathematical pun intended).

-- 
Peter Hunsberger

• References:
  • Re: Holographic XML
    • From: Hermann Stamm-Wilbrandt <STAMMW@d...>