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Home -> Community -> Usenet -> comp.databases.theory -> Re: What databases have taught me
Bob Badour wrote:
> I am speaking of data type as a concept. The integer data
> type has an unlimited number of operations defined on it.
> In most contexts, only a tiny subset of them are in scope.
What I don't get is why said unlimited number of operations defined /on/ integers are the definition /of/ integers. You and I can communicate using integers, prove theorems about integers, think about integers, etc by appealing only to a very small subset of those unlimited operations. So of what relevance are the remaining unmentioned or undiscovered operations to our discussion and thinking?
And suppose we define integers in the usual set theoretic or algebraic ways. Why can we not treat other operations as simply derived or auxiliary? How is it useful to think of them as defining integers?