# Re: Relations as primitive

From: Bob Badour <bbadour_at_pei.sympatico.ca>

Date: Fri, 11 Jan 2008 16:21:51 -0400

Message-ID: <4787cfe4$0$19873$9a566e8b_at_news.aliant.net>

> The mathematical idea of functions is the set of ordered

Date: Fri, 11 Jan 2008 16:21:51 -0400

Message-ID: <4787cfe4$0$19873$9a566e8b_at_news.aliant.net>

> 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