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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?
Paul wrote:
>
>So by analogy, if it's good enough for relvars to have an unbounded
>number of tuples, why shouldn't it be OK for domains to be able to
>have an unbounded number of values?
Very good question. The answer is that the unboundedness of the domain is not really the problem, but rather that some elements of the domain require an infinitely large representation. For example, every rational number can be represented by two finite natural numbers, but not all real numbers can be represented in a finite way (otherwise they would be enumerable and Cantor says we can't). As a consequence there will always be rounding errors unless you limit yourself to a specific recursive subset of the reals.