如何通过关系代数找到MAX？

(A x A) - (select 'a1' < 'a2') ((rename 'a' as 'a1')(A) x (rename 'a' as 'a2')(A))

project

A x A - (select 'a1' < 'a2') ((rename 'a' as 'a1')(A) x (rename 'a' as 'a2')(A))

project(a)A - project(a1)((select 'a1' < 'a2') ((rename 'a' as 'a1')(A) x (rename 'a' as 'a2')(A)))

A

1
2
3

A1
1
2
3

A2
1
2
3

A2<A1

join_{A2<A1}

A2<A1

1|2
1|3
2|3

join

a2<a1

A2
1
2

A diff A2

A
1
2
3

 diff

A2
1
2

3

SELECT

PROJECT

MINUS

RENAME

SELECT v1.number
FROM values v1
MINUS
SELECT v1.number
FROM values v1 JOIN values v2 ON v2.number > v1.number

1. First we want to PROJECT and RENAME relation A
2. We then to a THETA JOIN with the test a1<a2
3. We then PROJECT the result of the relation to give us a single set of values 
   a1: 1,2,3 (not max value since a1<a2)

4. We then apply the difference operator with the original relation so: 
   1,2,3,4 --- 1,2,3 returns 4

   4 is the Max value.

MAX

x

A

d

A

x

set difference

A

x

 Project x(A) - Project A.x
(Select A.x < d.x (A x Rename d(A)))