First normal form

First normal form (1NF) is a property of a relation in a relational database. A relation is in first normal form if and only if the domain of each attribute contains only atomic (indivisible) values, and the value of each attribute contains only a single value from that domain.[1] The first definition of the term, in a 1971 conference paper by Edgar Codd, defined a relation to be in first normal form when none of its domains have any sets as elements.[2]

First normal form is an essential property of a relation in a relational database. Database normalization is the process of representing a database in terms of relations in standard normal forms, where first normal is a minimal requirement.

First normal form enforces these criteria:[3]

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

Examples

The following scenarios first illustrate how a database design might violate first normal form, followed by examples that comply.

Designs that violate 1NF

Below is a table that stores the names and telephone numbers of customers. One requirement though is to retain multiple telephone numbers for some customers. The simplest way of satisfying this requirement is to allow the "Telephone Number" column in any given row to contain more than one value:

Customer
Customer ID	First Name	Surname	Telephone Number
123	Pooja	Singh	555-861-2025, 192-122-1111
456	San	Zhang	(555) 403-1659 Ext. 53; 182-929-2929
789	John	Doe	555-808-9633

The telephone number column contains multiple phone numbers in a single value. For example, the first row has two telephone numbers separated by a comma. The column values are not atomic: it can be subdivided into two numbers. This violates first normal form.

An apparent solution is to introduce more columns:

Customer
Customer ID	First Name	Surname	Telephone Number1	Telephone Number2
123	Pooja	Singh	555-861-2025	192-122-1111
456	San	Zhang	(555) 403-1659 Ext. 53	182-929-2929
789	John	Doe	555-808-9633

Technically, this table does not violate the requirement for values to be atomic. However, informally, the two telephone number columns still form a "repeating group": they repeat what is conceptually the same attribute, namely a telephone number. An arbitrary and hence meaningless ordering has been introduced: why is 555-861-2025 put into the Telephone Number1 column rather than the Telephone Number2 column? There's no reason why customers could not have more than two telephone numbers, so how many Telephone NumberN columns should there be? It is not possible to search for a telephone number without searching an arbitrary number of columns. Adding an extra telephone number may require the table to be reorganized by the addition of a new column rather than just having a new row (tuple) added. (The null value for Telephone Number2 for customer 789 is also an issue.)

Designs that comply with 1NF

To bring the model into the first normal form, we split the strings we used to hold our telephone number information into "atomic" (i.e. indivisible) entities: single phone numbers. And we ensure no row contains more than one phone number.

Customer
Customer ID	First Name	Surname	Telephone Number
123	Pooja	Singh	555-861-2025
123	Pooja	Singh	192-122-1111
456	San	Zhang	182-929-2929
456	San	Zhang	(555) 403-1659 Ext. 53
789	John	Doe	555-808-9633

Note that the "ID" is no longer unique in this solution with duplicated customers. To uniquely identify a row, we need to use a combination of (ID, Telephone Number). The value of the combination is unique although each column separately contains repeated values. Being able to uniquely identify a row (tuple) is a requirement of 1NF.

An alternative design uses two tables:

Customer Name
Customer ID	First Name	Surname
123	Pooja	Singh
456	San	Zhang
789	John	Doe

Customer Telephone Number
Telephone Number ID	Customer ID	Telephone Number
1	123	555-861-2025
2	123	192-122-1111
3	456	(555) 403-1659 Ext. 53
4	456	182-929-2929
5	789	555-808-9633

Columns do not contain more than one telephone number in this design. Instead, each Customer-to-Telephone Number link appears on its own row. Using Customer ID as key, a one-to-many relationship exists between the name and the number tables. A row in the "parent" table, Customer Name, can be associated with many telephone number rows in the "child" table, Customer Telephone Number, but each telephone number belongs to one, and only one customer. (In the "real" world, this would not be a good assumption.) It is worth noting that this design meets the additional requirements for second and third normal form.

Atomicity

Edgar F. Codd's definition of 1NF makes reference to the concept of 'atomicity'. Codd states that the "values in the domains on which each relation is defined are required to be atomic with respect to the DBMS."[4] Codd defines an atomic value as one that "cannot be decomposed into smaller pieces by the DBMS (excluding certain special functions)"[5] meaning a column should not be divided into parts with more than one kind of data in it such that what one part means to the DBMS depends on another part of the same column.

Hugh Darwen and Chris Date have suggested that Codd's concept of an "atomic value" is ambiguous, and that this ambiguity has led to widespread confusion about how 1NF should be understood.[6][7] In particular, the notion of a "value that cannot be decomposed" is problematic, as it would seem to imply that few, if any, data types are atomic:

A character string would seem not to be atomic, as the RDBMS typically provides operators to decompose it into substrings.
A fixed-point number would seem not to be atomic, as the RDBMS typically provides operators to decompose it into integer and fractional components.
An ISBN would seem not to be atomic, as it includes language and publisher identifier.

Date suggests that "the notion of atomicity has no absolute meaning":[8][9] a value may be considered atomic for some purposes, but may be considered an assemblage of more basic elements for other purposes. If this position is accepted, 1NF cannot be defined with reference to atomicity. Columns of any conceivable data type (from string types and numeric types to array types and table types) are then acceptable in a 1NF table—although perhaps not always desirable; for example, it may be more desirable to separate a Customer Name column into two separate columns as First Name, Surname.

1NF tables as representations of relations

According to Date's definition, a table is in first normal form if and only if it is "isomorphic to some relation", which means, specifically, that it satisfies the following five conditions:[10]

There's no top-to-bottom ordering to the rows.

There's no left-to-right ordering to the columns.

There are no duplicate rows.

Every row-and-column intersection contains exactly one value from the applicable domain (and nothing else).

All columns are regular [i.e. rows have no hidden components such as row IDs, object IDs, or hidden timestamps].

Violation of any of these conditions would mean that the table is not strictly relational, and therefore that it is not in first normal form.

Examples of tables (or views) that would not meet this definition of first normal form are:

A table that lacks a unique key constraint. Such a table would be able to accommodate duplicate rows, in violation of condition 3.
A view whose definition mandates that results be returned in a particular order, so that the row-ordering is an intrinsic and meaningful aspect of the view. (Such views cannot be created using SQL that conforms to the SQL:2003 standard.) This violates condition 1. The tuples in true relations are not ordered with respect to each other.
A table with at least one nullable attribute. A nullable attribute would be in violation of condition 4, which requires every column to contain exactly one value from its column's domain. This aspect of condition 4 is controversial. It marks an important departure from Codd's later vision of the relational model,[11] which made explicit provision for nulls.[12] First normal form, as defined by Chris Date, permits relation-valued attributes (tables within tables). Date argues that relation-valued attributes, by means of which a column within a table can contain a table, are useful in rare cases.[13]

References

Elmasri, Ramez; Navathe, Shamkant B. (July 2003). Fundamentals of Database Systems (Fourth ed.). Pearson. p. 315. ISBN 0321204484. It states that the domain of an attribute must include only atomic (simple, indivisible) values and that the value of any attribute in a tuple must be a single value from the domain of that attribute.
Codd, E. F. (October 1972). Further normalization of the database relational model. Data Base Systems. Courant Institute: Prentice-Hall. ISBN 013196741X. A relation is in first normal form if it has the property that none of its domains has elements which are themselves sets.
Watt, Adrienne; Eng, Nelson (2014). Database Design (2nd ed.). Victoria, B.C: BCcampus.
Codd, E. F. The Relational Model for Database Management Version 2 (Addison-Wesley, 1990).
Codd, E. F. The Relational Model for Database Management Version 2 (Addison-Wesley, 1990), p. 6.
Darwen, Hugh. "Relation-Valued Attributes; or, Will the Real First Normal Form Please Stand Up?", in C. J. Date and Hugh Darwen, Relational Database Writings 1989-1991 (Addison-Wesley, 1992).
Date, C. J. (2007). What First Normal Form Really Means. Date on Database: Writings 2000–2006. Apress. p. 108. ISBN 978-1-4842-2029-0. '[F]or many years,' writes Date, 'I was as confused as anyone else. What's worse, I did my best (worst?) to spread that confusion through my writings, seminars, and other presentations.'
Date, C. J. (2007). What First Normal Form Really Means. Date on Database: Writings 2000–2006. Apress. p. 112. ISBN 978-1-4842-2029-0.
Date, C. J. (6 November 2015). SQL and Relational Theory: How to Write Accurate SQL Code. O'Reilly Media. pp. 50–. ISBN 978-1-4919-4115-7. Retrieved 31 October 2018.
Date, C. J. (2007). What First Normal Form Really Means. Date on Database: Writings 2000–2006. Apress. pp. 127–128. ISBN 978-1-4842-2029-0.
Date, C. J. (2009). "Appendix A.2". SQL and Relational Theory. O'Reilly. Codd first defined the relational model in 1969 and didn't introduce nulls until 1979
Date, C. J. (October 14, 1985). "Is Your DBMS Really Relational?". Computerworld. Null values ... [must be] supported in a fully relational DBMS for representing missing information and inapplicable information in a systematic way, independent of data type. (the third of Codd's 12 rules)
Date, C. J. (2007). What First Normal Form Really Means. Date on Database: Writings 2000–2006. Apress. pp. 121–126. ISBN 978-1-4842-2029-0.