The mathematical concept underlying the relational model is
the set-theoretic *relation* which is a
subset of the Cartesian product of a list of domains. This
set-theoretic relation gives the model its name (do not confuse
it with the relationship from the *Entity-Relationship model*). Formally a domain is
simply a set of values. For example the set of integers is a
domain. Also the set of character strings of length 20 and the
real numbers are examples of domains.

The *Cartesian product* of domains
`D _{1}`,

For example, when we have `k`=2,
`D _{1}`=

A Relation is any subset of the Cartesian product of one or
more domains: `R` ⊆ `D _{1}` ×

For example `{(0,a),(0,b),(1,a)}` is a
relation; it is in fact a subset of `D _{1}` ×

The members of a relation are called tuples. Each relation of
some Cartesian product `D _{1}` ×

A relation can be viewed as a table (as we already did,
remember The Suppliers and
Parts Database where every tuple is represented by a row and
every column corresponds to one component of a tuple. Giving
names (called attributes) to the columns leads to the definition
of a *relation scheme*.

A *relation scheme* `R` is a finite set of attributes `A _{1}`,

Note:Arelation schemeis just a kind of template whereas arelationis an instance of arelation scheme. The relation consists of tuples (and can therefore be viewed as a table); not so the relation scheme.

We often talked about *domains* in
the last section. Recall that a domain is, formally, just a set
of values (e.g., the set of integers or the real numbers). In
terms of database systems we often talk of *data types* instead of domains. When we define a
table we have to make a decision about which attributes to
include. Additionally we have to decide which kind of data is
going to be stored as attribute values. For example the values
of `SNAME` from the table `SUPPLIER` will be character strings, whereas
`SNO` will store integers. We define
this by assigning a data type to each attribute. The type of
`SNAME` will be `VARCHAR(20)` (this is the SQL type for character strings of length <=
20), the type of `SNO` will be
`INTEGER`. With the assignment of a data
type we also have selected a domain for an attribute. The
domain of `SNAME` is the set of all
character strings of length <= 20, the domain of `SNO` is the set of all integer numbers.

If you see anything in the documentation that is not correct, does not match your experience with the particular feature or requires further clarification, please use this form to report a documentation issue.