John,

Lurker here jumping in ... :-)

2nd NF: All attributes in the entity are dependant on the entire primary key.

Example;

Invoice Detail Lines Entity

Structure:

Fields
InvoiceNumber (PK part 1)
LineNumber (PK part 2)
CustomerID (non-key attribute)
...

The 2nd NF is violated because the CustomerID is NOT dependant on the ENTIRE PK of the entity, it is dependant only on part of it (InvoiceNumber) and is unaffected by the other part (LineNumber).

OK, that's for 2nd Normal Form.

You are correct in that the entire process of normalization tends to remove redundant data from the design, however, there is no Normal Form that states anything directly about redundant data.

Of course 1st NF says, there are no multi-valued or repeating attributes in the entity's structure. This rule does require that one look at the domain for each attribute in order to know if it is a repeating attribute or not (two attributes with the same domain are repeating).

The problem with your original example way back up the line was that the two fields you chose as your example were not redundant as they had different domains definitions. One was the current address and the other was the address at the time of the invoice.

The same problem arises when you consider tax rates. Your have a tax rate field in the customer table that is the customer's current tax rate and there is a tax rate field in the invoice table that is the tax rate at the time of the invoice. Do these two fields represent a denormalized structure? Are they redundant data storage? No they are neither as they have completely different domain definitions and therefore are completely different pieces of data.