Re: Proposal: 6NF
Date: Sat, 21 Oct 2006 20:44:13 -0400
Message-ID: <87wt6t18o2.fsf_at_wolfe.cbbrowne.com>
After a long battle with technology, paul c <toledobythesea_at_dbms.yuc>, an earthling, wrote:
> 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!
-- wm(X,Y):-write(X),write('_at_'),write(Y). wm('cbbrowne','gmail.com'). http://linuxdatabases.info/info/slony.html "Let me blow that up a bit more for you." -- Colin Powell, Discussing a picture of the intelligence compound in IraqReceived on Sun Oct 22 2006 - 02:44:13 CEST