However, if the employee name in the function is not Daniel Smith but the employee is in marketing, the first predicate is true. How does that fit into relational databases?
The arrow notation here is not material implication, but function evaluation. The function itself can be interpreted as an Indicator Function[1] for the employee set, or alternatively, as simply evaluating the predicate.
In terms of tables, the rows are exactly the subset of predicates that are TRUE. So FALSE statements like the second one are indicated by their absence in the employee table.
In mathematics, a relation is a set of ordered pairs.
Strictly speaking, the relations of database theory are different objects, but closely related. (Yes, I just made an awesome pun.)
I'm surprised that the author didn't include "a relation is a set of tuples" as a definition in the article. Also, absolutely nothing is said about viewing a relation as a graph.
I suspect that using unordered sets as the foundation for databases might have been a mistake, and ordered lists with allowed repetition would've made a better model, if only because they can model tables and query results equally well (ORDER BY, SELECT without DISTINCT). Is there a good reason why this road was not taken?
In most actual implementations of relational DBs there's nothing to disallow repetition in a table - you just don't specify a primary key (or preferably have a unique primary key that's just an ignored surrogate).
The difficulty with caring about ordering in the relational model is that suddenly you're imposing a lot more constraints: when you're joining two tables, whose order 'wins'? If you say (for example) that left side wins, you then need to keep track of that order through your query.
Upon consideration, this article is really just a bunch of intellectual masturbation. A set is a function mapping from the universal set to true|false. A relation is a function mapping from some tuple space to true|false. No generalization of functions required.
"The self is a relation that relates itself to itself or is the relation's relating itself to itself in the relation; the self is not the relation but is the relation's relating itself to itself." - Kierkgaard
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[ 2.6 ms ] story [ 25.5 ms ] threadP.S. Great article!
In terms of tables, the rows are exactly the subset of predicates that are TRUE. So FALSE statements like the second one are indicated by their absence in the employee table.
[1] http://en.wikipedia.org/wiki/Indicator_function
Strictly speaking, the relations of database theory are different objects, but closely related. (Yes, I just made an awesome pun.)
I'm surprised that the author didn't include "a relation is a set of tuples" as a definition in the article. Also, absolutely nothing is said about viewing a relation as a graph.
The difficulty with caring about ordering in the relational model is that suddenly you're imposing a lot more constraints: when you're joining two tables, whose order 'wins'? If you say (for example) that left side wins, you then need to keep track of that order through your query.
Sorry, had to chime in with that