Missing Information & Empty Sets.

I have been doing a bit of thinking about the Missing Information problem in both SQL and TRDBM systems

and would like some feedback in relation (pun intended) to those thoughts.

Assume a simple Customer - Order schema

Customer (Customer# INT) KEY (Customer#)

Order (Order# INT, Customer# INT) KEY (Order#) FOREIGN KEY (Customer.Customer#)

The Customer# domain is a set of unsigned integers from 1 -> INT.MAX

Lets assume that the Customer relation has no tuples ie: is a empty set.

The domain for the Customer# attribute in the Customer relation is still 1 -> INT.MAX Now here is where I sink or swim........

BUT the domain for the Customer# attribute in the Order relation is effectively an empty set

due to the RI constraint. The domain "grows" as tuples are added to the Customer table.

So from there I have a couple of questions

1. Is an empty set of type X a valid value of the domain X?
2. Does an empty set of type X violate 1NF?

So in context it boils down to this question...

Can I insert an empty set (with the relevant empty-set types) into the Order table without violating RI?

If the answer is YES then could we not simply use an empty-set as the Missing Information marker?

I got these thoughts from TABLE_DEE and TABLE_DUM as outlined in TTM but unfortunately

my copy is currently 1200Km away and I am struggling to remember there definitions correctly.

All criticism welcome however harsh.......

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