Re: Proposal: 6NF
Date: Sat, 21 Oct 2006 22:30:21 GMT
Message-ID: <1cx_g.168545$5R2.48234_at_pd7urf3no>
Christopher Browne wrote:
> Quoth "Keith H Duggar" <duggar_at_alum.mit.edu>:
>> vc wrote: >>> Marshall wrote: >>>> I do not recall learning anything in secondary school >>>> which would suggest 2 and 2.0 were numerically different >>>> in any way. Nor can I think of any *arithmetic* way to >>>> distinguish between 2 and 2.0. >>> You have to construct all the real numbers and prove that >>> 2 is an element of the set. >> Any mathematical number construct that fails to equate 2.0 >> and 2, fails to model our most basic common sense or >> "elemntary school" concept of the number 2.
>
> In abstract algebra, you get groups and other structures where 2 may
> be a meaningful value, but 2.0 isn't, because there isn't any inherent
> notion of fractional values. Indeed, in the realm of discrete
> mathematics, it's unmeaningful (even undesirable!) to have any values
> lying between 1 and 2 and 2 and 3.
>
> Proof by induction, for instance, depends on the notion that there are
> no intermediate values.
>
> I don't think that "elemntary school" concepts are of any particular
> relevance when looking at mathematical structures; they are what they
> are, irrespective of whether a layman can relate them to anything that
> seems familiar to the layman.
Right Christopher, I think some elementary school concepts can be quite misleading as there are very few teachers at that level who know much about math. For a little more well-thought-out look at basic concepts, the book I like is "introduction to mathematical philosophy" which was written by Bertrand Russell after he was disappointed by the low sales of the opus he wrote with Whitehead. Somewhere it's said that his angle was to aim it at the layman (so as to get more sales - this was in the days when every English town of any size had a scientific society that gave free lectures at night) and since I'm a layman when it comes to math, I'd say he succeeded. It is a charming little book, I believe still in print. One of its main themes concerns "what is a number?" but there are others intertwined notably "what is a relation".
When I first came across it, I couldn't help but notice that many of the chapter titles might be said to be ideal ones for a book on database theory. He wrote it (while in jail) in 1917!
paul c
ps: Christopher, I remember you from years ago at the tlug meetings (before they kicked me out for trying to give away some core memory for free) - hope you are still enjoying the finite automata book - there were only two chapters I could understand, so I photocopied them and still have them! Received on Sun Oct 22 2006 - 00:30:21 CEST