Re: Is a function a relation?
Date: Tue, 23 Jun 2009 20:19:22 -0700 (PDT)
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
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.
Not my favorite way of thinking about the world, but it's mathematically sound.
Marshall Received on Tue Jun 23 2009 - 22:19:22 CDT