Re: Proposal: 6NF

Christopher Browne wrote:
> 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!

I have never understood what beauty has to do with mathematics and vice versa and I hope I never do as I feel that would make me less human and my aim is to become more so.

p

>> 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!