# Re: Is a function a relation?

Date: Tue, 23 Jun 2009 23:43:17 -0700 (PDT)

Message-ID: <d87e4ac9-6a5a-4208-a39c-9feb676f7c53_at_q3g2000pra.googlegroups.com>

On Jun 24, 11:19 am, Marshall <marshall.spi..._at_gmail.com> wrote:

> On Jun 22, 11:14 pm, David BL <davi..._at_iinet.net.au> wrote:

*>
**> > On Jun 23, 1:35 pm, David BL <davi..._at_iinet.net.au> wrote:
**>
**> > > Yes that's one way of looking at it.
**>
**> > I'll expand on what I mean by that. It seems to me that one could use
**> > special conventions to "show" that just about any type can be regarded
**> > as a specialisation of a relation. E.g. one could say that a whole
**> > number in [0,255] is a relation by introducing symbols to represent
**> > 1,2,4,8,...,128 and the relation records a set of symbols that are
**> > then interpreted in the manner of an 8 bit unsigned representation.
**>
**> Heh. Yes, there is a bijection between the natural numbers and
**> bit strings. But the tricky thing is, bit strings are strings, which
**> is
**> to say they are lists, which is to say they are indexed by natural
**> numbers.
**>
**> Axiomatic set theory just uses sets. And I mean it *really*
**> just uses sets; there are no other kinds of objects in that
**> universe. Natural numbers are encoded as sets. Everything
**> is encoded as sets. If you have a set, every member of the
**> set is itself a set.
*

Good point. These are called pure or hereditary sets.

http://en.wikipedia.org/wiki/Pure_set

> Not my favorite way of thinking about the world, but it's

*> mathematically sound.
*

Received on Wed Jun 24 2009 - 08:43:17 CEST