Re: Is a function a relation?

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