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

Date: Fri, 14 Feb 2003 00:49:10 -0500

Message-ID: <b2hvtk$n08$1_at_slb6.atl.mindspring.net>

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