Note: To demonstrate the correctness and stability due to a sound theoretical foundation relative to the industry's fad-driven "cookbook" practices, I am re-publishing as "Oldies But Goodies" material from the old DBDebunk.com (2000-06), so that you can judge for yourself how well my arguments hold up and whether the industry has progressed beyond the misconceptions those arguments were intended to dispel. I may revise, break into parts, and/or add comments and/or references.

This is an email exchange with readers in response to my article Normalization and Performance: Never the Twain Shall Meet.

Revised 3/20/21

I recently came across a review of Edsger Dijkstra's work, where the following comment on a book he co-authored (referred to as D&S) raised my debunking antennae:

“... in general computer people seem to have a penchant for whipping up homebrew logics ... D&S is not the only example ... See E.F. Codd’s Relational Calculus, an obvious mess.”
--Maarten van Emden, A Bridge too Far: E.W. Dijkstra and Logic 

Having recently argued that "Codd was wrong" and "You're teaching [his] gospel" Betray Lack of Foundation Knowledge, my suspicion should hardly surprise. Besides, criticism of Dijkstra is a very tall order in itself, particularly in the context of disputes among logicians). As a reader asked, "What’s so obviously messy in Codd’s Relational Calculus?". Answer:

Note: Each "Test Your Foundation Knowledge" post presents one or more misconceptions about data fundamentals. To test your knowledge, first try to detect them, then proceed to read our debunking, reflecting the current understanding of the RDM, distinct from whatever has passed for it in the industry to date. If there isn't a match, you can review references -- reflecting the current understanding of the RDM, distinct from whatever has passed for it in the industry to date -- which explain and correct the misconceptions. You can acquire further knowledge by checking out our POSTS, BOOKS, PAPERS, LINKS (or, better, organize one of our on-site SEMINARS, which can be customized to specific needs).

“A relation, or table, in a relational database ... must have a set of columns or attributes, and it must have a set of rows to contain the data. A tuple (or row) can be a duplicate. In practice, a database might actually contain duplicate rows, but there should be practices in place to avoid this, such as the use of unique primary keys (next up). Given that a tuple cannot be a duplicate, it follows that a relation must contain at least one attribute (or column) that identifies each tuple (or row) uniquely. This is usually the primary key. This primary key cannot be duplicated.”

Misconceptions

• A relation is not a table and, thus, has neither fields, nor columns (which are not attributes) and rows;
• "Duplicate tuples" is a contradiction in terms -- a table with duplicate rows does not visualize a relation (i.e., is not a R-table) -- and a database with duplicated data is not relational;
• Without PKs a relation is not semantically consistent (i.e. it does not faithfully represent group of entities, which are distinguishable in the real world);

Fundamentals

• A database relation

- is a relationship among domains (sets of values) -- a subset of their cross-product -- a set of tuples (sets of values drawn from the domains) or, in other words, a set of sets from sets;
- has attributes, which are representations (1:1 mappings) of the domains in the relation;
- is semantically constrained to be consistent with (i.e., represent faithfully) the entity group in the conceptual model it represents in the database.

• A R-table visualizes a relation on some physical medium -- it plays no part in the relational model.

• Absence of PKs is semantic inconsistency with (inaccurate representation of) reality and a violation of the RDM.
  

Further Reading

What Relations Really Are and Why They Are Important

Understanding Relations series

What Is a Relational Database

Duplicates: Stating the Same Fact More Than Once Does Not Make it Truer, Only Redundant