09/19/23: For the latest on this subject see: FIRST NORMAL FORM - A DEFINITIVE GUIDE
Note: This is a 11/23/17 revision of Part 1 of a three-part series that replaced all of my previous posts on the subject (pages of which redirect here), in order to further tighten integration with the McGoveran formalization and interpretation [1] of Codd's true RDM.
On the one hand:
"... there is no generally accepted definition of 1NF ... the word that you see most often is 'atomic'. It is common to say that a relation is in 1NF if all its attributes [sic] are atomic ... Does 1NF equate to atomic attribute [values]? ... what [do] people have in mind [when they claim] atomicity? ... the [meaning] behind definitions is that you should rarely need to extract information from a value of an attribute ... But that explains why one cannot decide, depending on theory only, whether a relation is in 1NF ... it is a habitual use of data that makes attributes atomic, not theory. No wonder, there is so much mess in theory about what 1NF should be."
--What is the actual definition of First Normal Form, Vertabelo.com
On another, according to a DBDebunk reader:
"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)!"
All sorts of other definitions proliferate, for example:
"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
Note: A relational databases consists of relations that can be visualized as R-tables. Normal forms are a property of relations, not R-tables -- a "R-table in 1NF" is shorthand for consistency with the underlying relation.