# Re: Extending my question. Was: The relational model and relational algebra - why did SQL become the industry standard?

Date: Tue, 18 Feb 2003 14:32:23 -0800

Message-ID: <lBy4a.20$h_3.142_at_news.oracle.com>

"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 - 23:32:23 CET