"Codd in 1969/70 (and RM V/2 20 years later) gave a precise, theory-based definition of "atomic" aka "simple" aka "non-decomposable" (later aka non-"compound" aka non-"structured"): not relation-valued. And he gave a precise definition of "normalized" (1NF): relations free of relation-valued-domains (RVD)!"

 "First normal form enforces these criteria:

- Eliminate repeating groups in individual tables.
- Create a separate table for each set of related data.
-Identify each set of related data with a primary key."

--First normal form, Wikipedia

• 1NF: simple domains with values that are treated as atomic by the data sublanguage;
• Relations are (at least in) 1NF by definition (otherwise they are not relations);

• The original normal form is not the same as the current 1NF, except to say that the former is to the original join what the 5NF is to the current join;
• For logical validity, semantic correctness and data independence 1NF is insufficient -- relations must also be in 5NF by definition.

Simple Domains with Atomic Values

"So far, we have discussed examples of relations which are defined on simple domains -- domains whose elements are atomic (non-decomposable) values. Non-atomic values can be discussed within the relational framework. Thus, some domains may have relations as elements."

--E. F. Codd (1969)

• Unique, unordered n-valued tuples with atomic, non-missing values;
• Uniquely named, unordered attributes defined on simple domains;

==============================
 ID  NAME                 ADDRESS
====-------------------------------------
  1  Mark Tomers      56 Tomato Road
  2  Fred Askalong    3277 Hadley Drive
  3  May Anne Brice   225 Century Avenue
  ...
===============================

(1) If yes, the IP requires that each should be an attribute defined on a simple domain;
(2) If not, applications will not access them, so NAME and ADDRESS can each be defined on simple domains with (first,last) and (#,street) combinations as atomic values;

"For a while scientists thought that atoms were literally indivisible. Any representation of them would then be "atomic" (no pun intended). Then we discovered electrons and the nucleus and they were understood as atomic, at least until we discovered protons and neutrons. Now we talk about quarks and so on. Clearly, atomicity is not an intrinsic concept and it must be defined in the context of the relevant knowledge —and how the value will be used."

--David McGoveran

Repeating Groups

"Repeating groups (RG) originate with physical records in application files having no fixed number of fields (as in COBOL). The number of fields could be indicated by a special field count in the "record header", by a special “end of group” indicator value in the last field, or -- worse -- recorded only in the code that accessed those records. This same method was used at the field level: some fields -- like one-dimensional arrays, or lists -- contained multiple values or "sub-fields" and determining where the list ended could be tricky."

--David McGoveran