--- EDIT ---: (Previous previous incorrect tests removed)
The second attempt (not quite relational algebra).
This works, but only when the char (1) fields:
SELECT colA, colB, colC FROM mytable WHERE CONCAT(colA, colB, colC) BETWEEN CONCAT('A', 'B', 'C') AND CONCAT('D', 'E', 'F') ORDER BY colA, colB, colC LIMIT 1 ;
I thought that a view that shows all combinations of tuples from mytable that are less than or equal to tuples in the same table could be useful, as this can be used for other comparisons:
CREATE VIEW lessORequal AS ( SELECT a.colA AS smallA , a.colB AS smallB , a.colC AS smallC , b.colA AS largeA , b.colB AS largeB , b.colC AS largeC FROM mytable a JOIN mytable b ON (a.colA < b.colA) OR ( (a.colA = b.colA) AND ( (a.colB < b.colB) OR (a.colB = b.colB AND a.colC <= b.colC) ) ) ) ;
Using a similar technique, this solves the issue. It works with any fields (int, float, char of any length). It will be kind of awkard and harder, although if you try to add more fields.
SELECT colA, colB, colC FROM mytable m WHERE ( ('A' < colA) OR ( ('A' = colA) AND ( ('B' < colB) OR ('B' = colB AND 'C' <= colC) ) ) ) AND ( (colA < 'D') OR ( (colA = 'D') AND ( (colB < 'E') OR (colB = 'E' AND colC <= 'F') ) ) ) ORDER BY colA, colB, colC LIMIT 1 ;
You can also define a function:
CREATE FUNCTION IslessORequalThan( lowA CHAR(1) , lowB CHAR(1) , lowC CHAR(1) , highA CHAR(1) , highB CHAR(1) , highC CHAR(1) ) RETURNS boolean RETURN ( (lowA < highA) OR ( (lowA = highA) AND ( (lowB < highB) OR ( (lowB = highB) AND (lowC <= highC) ) ) ) );
and use it to solve the same or similar problems. This solves the issue again. The query is elegant, but if you change the type or number of fields, you must create a new function.
SELECT colA , colB , colC FROM mytable WHERE IslessORequalThan( 'A', 'B', 'C', colA, colB, colC ) AND IslessORequalThan( colA, colB, colC, 'D', 'E', 'F' ) ORDER BY colA, colB, colC LIMIT 1;
Until then, because the condition
(colA, colB, colC) BETWEEN ('A', 'B', 'C') AND ('D', 'E', 'F')
in MySQL was not allowed, I thought that
('A', 'B', 'C') <= (colA, colB, colC)
also not allowed. But I was wrong.