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Home -> Community -> Usenet -> comp.databases.theory -> Re: Extending my question. Was: The relational model and relationalalgebra - why did SQL become the industry standard?
"Lauri Pietarinen" <lauri.pietarinen_at_atbusiness.com> wrote in message news:3E4C1FF0.9020001_at_atbusiness.com...
In short, logic and set theory together are only a tiny part of mathematics.
Don't evangelize them.
Well, not being a mathematician,
but having studied some mathematics I was and
still am under the impression that all modern mathematics
is based on set theory which is equivalent with logic.
Set Reductionalism is a dicease that I was ill when being a student. Although Sets and Logic certainly spice mathematics with rigour, they are mostly irrelevant for practioner mathematician not working in those fields.
Here is a quote from Wikipedia
(http://www.wikipedia.org/wiki/Foundations_of_mathematics)
<quote>
The current dominant mathematical paradigm is based on axiomatic set theory and formal logic. Virtually all mathematical theorems today can be formulated as theorems of set theory. The truth of a mathematical statement, in this view, is then nothing but the claim that the statement can be derived from the axioms of set theory using the rules of formal logic.
<quote/>
There is a difference between "can" and "have to". Reductionalizm to sets might be unnatural, unpractical, etc. The famous example is the ordered pair definition
(a, b) := {{a}, {a, b}}
AFAIK, no mathematical theorem is reformulated to use the above set based definition instead of ordered pairs. Ordered tuple is widely considered to be a basic concept (including Relational Theory;-). Received on Thu Feb 13 2003 - 17:23:48 CST