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,

A Relation is any subset of the Cartesian product of one or more
domains: ` R` ⊆

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.