Finding the Maximum using Relational Algebra

We know that if you want to get the maximum value of a column in SQL, you can simply use the MAX function as shown below:

SELECT MAX(value) FROM T

You can also do it without the MAX function as follows:

SELECT T.* FROM T
MINUS
SELECT T.* FROM T, T as T2 WHERE T.value<T2.value

or:

SELECT T.* FROM T
LEFT JOIN T as T2 ON T.value<T2.value
WHERE T2.value IS NULL

Relational Algebra:
Using Relational Algebra (RA) syntax, this would be:

\project_{value}(T)
\diff
\project_{value} (
    \select_{value < value2}(
      \project_{value}(T)
      \cross
      \rename_{value2}(\project_{value}(T))
    )
)

where:

• \cross is the relational cross-product operator
• \diff is the relational diff operator
• \project_{attr_list} is the relational projection operator
• \rename_{new_attr_name_list} is the relational renaming operator
• \select_{cond} is the relational selection operator