Regarding ordering. Relations are defined to not be in a meaningful order. This doesn't mean you couldn't define some derivative that is ordered or that the r

Regarding ordering. Relations are defined to not be in a meaningful order. This doesn't mean you couldn't define some derivative that is ordered or that the relations might not be ordered in some way that is ignored by the relational math. Suppose we have a relation R. We may order this relation physically in order to help the computer retrieve data faster, clustering on an index for example. However, clustering on an index does not mean that we are guaranteed to get the same order back when we do a select * from.... (we probably will but we aren't guaranteed to). And if we add a join or other relational transformation, the order will probably not be the same. In other words, ordering is outside the scope of relational math per se. However that doesn't mean you can't have pre-ordered relations. It just means the ordering is meaningless as far as the math goes. The ordering may however be of great practical importance as the computer goes about grabbing the relevant tuples from the relation. Similarly I don't see a reason why ordering can't happen after the relational math is done either, in this case for humans. What this tells me is that the relational model is not entirely complete in itself in that ordering is an orthogonal consideration largely ignored which means there are certain questions you cannot answer directly with relational math (such select from R a relation L such that it includes the tuples with the five highest values of R(2) lower than 25. I think that's mostly what you are getting at. But that's a matter of relational math being incomplete for real-world scenarios, not SQL (since SQL implementations do provide for ordering).