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Home -> Community -> Usenet -> comp.databases.theory -> Re: Extending my question. Was: The relational model and relational algebra - why did SQL become the industry standard?
"Steve Kass" <skass_at_drew.edu> wrote in message
news:b2u9bg$50p$1_at_slb2.atl.mindspring.net...
> Mikito Harakiri wrote:
>
> >This is just a series of random definitions, well spiced with curly
> >bracketed symbols. Or is there any wonderful theory about it? Where in
math
> >did you see "We have 10 unrelated alternative definitions, pick anyone
you
> >like"?
> Um, everywhere? Pick up half a dozen graph theory textbooks,
> and you're likely to see nearly as many definitions. Some analysis
> books define irrationals in terms of Dedekind cuts, others with
> limits.
Plus there is nonstandard analysis. Each of these is like a separate theory, however.
Now when we write
(a,b)=def={{a},{a,b}}
what theory does it belong to? What can we deduce from this "definition"? How does it relate to
(a,b)=def2={a,{a,b}}
for example?
> Riemann integrals get defined in all kinds of ways.
I know only one.
> The
> function f(z) = e^z has plenty of useful definitions.
Deduced from each other.
> Fortunately,
> mathematics is well-enough founded that the many alternate definitions
> of a construct are provably equivalent. I would be surprised to
> hear any mathematician suggest that the existence of many equivalent
> foundational definitions of a concept indicates that the concept is
> useless. There is no "one way" to define a mathematical idea using
> sets.
>
> To throw away all of mathematics because there are equivalent
> formulations of ideas makes as much sense as to throw away
> numbers because Europeans, Chinese, and Arabs write them
> differently.
I think we agree on all that. We disagree upon how "well founded" or "well established" set reduction is. Received on Tue Feb 18 2003 - 16:32:23 CST