Re: Object-relational impedence
Date: Fri, 14 Mar 2008 16:34:20 -0700 (PDT)
Message-ID: <e2c4db01-a3fa-4599-8e0a-091f5ad46204_at_e23g2000prf.googlegroups.com>
On Mar 14, 9:32 am, "Dmitry A. Kazakov" <mail..._at_dmitry-kazakov.de> wrote:
>
> LOL. Dear you should really read something introductory on set theory, just
> in order to never post anything like that. The distinction between set and
> the elements of, plays a central role in modern mathematics.
If you read something *introductory* on set theory, you will in general see sets described using one set of terms, and elements of sets in different terms. (Although you won't necessarily see them described as belonging to distinct classes; it is usually left unspecified.) If you get past the introductory phase, however, the distinction evaporates. The specific axiomatic set theory that could most be said to play a central role is modern mathematics is ZFC, an axiomatic theory which does not admit the existence of anything that is *not* a set. *Every* element of every set in ZFC is itself a set; numbers are encoded as sets, etc.
Of course there are less popular axiomatic theories such as Quine's New Foundations, which has a variant, NFU, which *does* draw a formal distinction between sets and elements. But by and large, the distinction between sets and elements does not exist in modern mathematics.
Marshall Received on Sat Mar 15 2008 - 00:34:20 CET