

From: Steve Kass <>
Date: Fri, 14 Feb 2003 00:49:10 -0500
Message-ID: <b2hvtk$n08$>

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
> 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

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