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Home -> Community -> Usenet -> comp.databases.theory -> 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!
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