In mathematics, a relation is a set of ordered pairs.<p>Strictly speaking, the relations of database theory are different objects, but closely related. (Yes, I just made an awesome pun.)<p>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?
The followup article (<a href="http://merrigrove.blogspot.com/2013/12/the-occultation-of-relations-and-logic_22.html?m=1" rel="nofollow">http://merrigrove.blogspot.com/2013/12/the-occultation-of-re...</a>) is really good, too. I particularly liked the concrete example of the "projection".
"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<p>Sorry, had to chime in with that
You have the following material implications:<p><pre><code> EMPLOYEE(Daniel Smith, Marketing) → TRUE
EMPLOYEE(Jebediah Vargas, Marketing) → FALSE
</code></pre>
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?<p>P.S. Great article!