Re: Extending my question. Was: The relational model and relationalalgebra - why did SQL become the industry standard?

Mikito Harakiri wrote:

>
> There is a difference between "can" and "have to". Reductionalizm to
> sets might be unnatural, unpractical, etc. The famous example is the
> ordered pair definition
>
> (a, b) := {{a}, {a, b}}
>
> AFAIK, no mathematical theorem is reformulated to use the above set
> based definition instead of ordered pairs. Ordered tuple is widely
> considered to be a basic concept (including Relational Theory;-).

That's why Lauri quoted a statement that said "can", not "have to".

I don't think mathematicians usually take any new notation as basic and not needing a definition as a set until they make sure there is a consistent set-theoretic definition. Once that is done (once), there may never be a need to resort to manipulating the underlying sets, as is typically the case with ordered pairs.

If you haven't read it, read Don Knuth's book "Surreal Numbers," which I think makes a nice case for never forgetting the connections to set theory.

Steve Received on Fri Feb 14 2003 - 06:49:10 CET