Re: Relations as primitive
Date: Fri, 11 Jan 2008 16:21:51 -0400
Message-ID: <4787cfe4$0$19873$9a566e8b_at_news.aliant.net>
Marshall wrote:
> On Jan 11, 12:54 am, David BL <davi..._at_iinet.net.au> wrote:
>
>>[...]
>
>
> The mathematical idea of functions is the set of ordered
> pairs, where the left item in the pair is a member of the
> domain and the right item is a member of the range.
> The domain can then be considered also to be ordered
> pairs, so that + then looks like
>
> {((1,1),2), ((2,2),4) ... }
>
> And so on. This is a consequence of the foundational
> approach in which sets are the basic building blocks.
> (And ordered pairs are defined in terms of sets, via
> Kuratowski or whatever.)
>
> However there is another way to go, which I first
> encountered in ch. 4 of TTM, and which I don't see
> discussed much or at all in mathematical circles,
> and which I find immensely appealing. The approach
> is to work directly with relations. So + looks like
>
> {(x=1, y=1, z=2), (x=2, y=2, z=4) ...}
>
> In point of fact, there is almost nothing of significance
> to this idea; it's equivalent to the usual formulation.
> But I nonetheless find the idea appealing of thinking
> about the foundations of mathematics in terms of
> taking relations as primitive rather than sets.
Relations are sets. Received on Fri Jan 11 2008 - 21:21:51 CET