set enable_seqscan=off;
CREATE TABLE test_timestamptz (
	i timestamptz
);
INSERT INTO test_timestamptz VALUES
	( '2004-10-26 03:55:08' ),
	( '2004-10-26 04:55:08' ),
	( '2004-10-26 05:55:08' ),
	( '2004-10-26 08:55:08' ),
	( '2004-10-27 09:55:08' ),
	( '2004-10-27 10:55:08' )
;
CREATE INDEX idx_timestamptz ON test_timestamptz USING gin (i);
SELECT * FROM test_timestamptz WHERE i<'2004-10-26 08:55:08'::timestamptz ORDER BY i;
              i               
------------------------------
 Tue Oct 26 03:55:08 2004 PDT
 Tue Oct 26 04:55:08 2004 PDT
 Tue Oct 26 05:55:08 2004 PDT
(3 rows)

SELECT * FROM test_timestamptz WHERE i<='2004-10-26 08:55:08'::timestamptz ORDER BY i;
              i               
------------------------------
 Tue Oct 26 03:55:08 2004 PDT
 Tue Oct 26 04:55:08 2004 PDT
 Tue Oct 26 05:55:08 2004 PDT
 Tue Oct 26 08:55:08 2004 PDT
(4 rows)

SELECT * FROM test_timestamptz WHERE i='2004-10-26 08:55:08'::timestamptz ORDER BY i;
              i               
------------------------------
 Tue Oct 26 08:55:08 2004 PDT
(1 row)

SELECT * FROM test_timestamptz WHERE i>='2004-10-26 08:55:08'::timestamptz ORDER BY i;
              i               
------------------------------
 Tue Oct 26 08:55:08 2004 PDT
 Wed Oct 27 09:55:08 2004 PDT
 Wed Oct 27 10:55:08 2004 PDT
(3 rows)

SELECT * FROM test_timestamptz WHERE i>'2004-10-26 08:55:08'::timestamptz ORDER BY i;
              i               
------------------------------
 Wed Oct 27 09:55:08 2004 PDT
 Wed Oct 27 10:55:08 2004 PDT
(2 rows)

explain (costs off)
SELECT * FROM test_timestamptz WHERE i<'2004-10-27'::date ORDER BY i;
                     QUERY PLAN                     
----------------------------------------------------
 Sort
   Sort Key: i
   ->  Bitmap Heap Scan on test_timestamptz
         Recheck Cond: (i < '10-27-2004'::date)
         ->  Bitmap Index Scan on idx_timestamptz
               Index Cond: (i < '10-27-2004'::date)
(6 rows)

SELECT * FROM test_timestamptz WHERE i<'2004-10-27'::date ORDER BY i;
              i               
------------------------------
 Tue Oct 26 03:55:08 2004 PDT
 Tue Oct 26 04:55:08 2004 PDT
 Tue Oct 26 05:55:08 2004 PDT
 Tue Oct 26 08:55:08 2004 PDT
(4 rows)

SELECT * FROM test_timestamptz WHERE i<='2004-10-27'::date ORDER BY i;
              i               
------------------------------
 Tue Oct 26 03:55:08 2004 PDT
 Tue Oct 26 04:55:08 2004 PDT
 Tue Oct 26 05:55:08 2004 PDT
 Tue Oct 26 08:55:08 2004 PDT
(4 rows)

SELECT * FROM test_timestamptz WHERE i='2004-10-27'::date ORDER BY i;
 i 
---
(0 rows)

SELECT * FROM test_timestamptz WHERE i>='2004-10-27'::date ORDER BY i;
              i               
------------------------------
 Wed Oct 27 09:55:08 2004 PDT
 Wed Oct 27 10:55:08 2004 PDT
(2 rows)

SELECT * FROM test_timestamptz WHERE i>'2004-10-27'::date ORDER BY i;
              i               
------------------------------
 Wed Oct 27 09:55:08 2004 PDT
 Wed Oct 27 10:55:08 2004 PDT
(2 rows)

explain (costs off)
SELECT * FROM test_timestamptz WHERE i<'2004-10-26 08:55:08'::timestamp ORDER BY i;
                                       QUERY PLAN                                        
-----------------------------------------------------------------------------------------
 Sort
   Sort Key: i
   ->  Bitmap Heap Scan on test_timestamptz
         Recheck Cond: (i < 'Tue Oct 26 08:55:08 2004'::timestamp without time zone)
         ->  Bitmap Index Scan on idx_timestamptz
               Index Cond: (i < 'Tue Oct 26 08:55:08 2004'::timestamp without time zone)
(6 rows)

SELECT * FROM test_timestamptz WHERE i<'2004-10-26 08:55:08'::timestamp ORDER BY i;
              i               
------------------------------
 Tue Oct 26 03:55:08 2004 PDT
 Tue Oct 26 04:55:08 2004 PDT
 Tue Oct 26 05:55:08 2004 PDT
(3 rows)

SELECT * FROM test_timestamptz WHERE i<='2004-10-26 08:55:08'::timestamp ORDER BY i;
              i               
------------------------------
 Tue Oct 26 03:55:08 2004 PDT
 Tue Oct 26 04:55:08 2004 PDT
 Tue Oct 26 05:55:08 2004 PDT
 Tue Oct 26 08:55:08 2004 PDT
(4 rows)

SELECT * FROM test_timestamptz WHERE i='2004-10-26 08:55:08'::timestamp ORDER BY i;
              i               
------------------------------
 Tue Oct 26 08:55:08 2004 PDT
(1 row)

SELECT * FROM test_timestamptz WHERE i>='2004-10-26 08:55:08'::timestamp ORDER BY i;
              i               
------------------------------
 Tue Oct 26 08:55:08 2004 PDT
 Wed Oct 27 09:55:08 2004 PDT
 Wed Oct 27 10:55:08 2004 PDT
(3 rows)

SELECT * FROM test_timestamptz WHERE i>'2004-10-26 08:55:08'::timestamp ORDER BY i;
              i               
------------------------------
 Wed Oct 27 09:55:08 2004 PDT
 Wed Oct 27 10:55:08 2004 PDT
(2 rows)