Empty Set Equality

SELECT 1 LIMIT 0;
Empty set (0.00 sec)

SELECT 2 LIMIT 0;
Empty set (0.00 sec)

SELECT NULL LIMIT 0;
Empty set (0.00 sec)

Exactly what I’d expect. So here’s the question:

SELECT '1 = 1' AS equality, (SELECT 1 LIMIT 0) = (SELECT 1 LIMIT 0) AS result
UNION SELECT '1 = 2', (SELECT 1 LIMIT 0) = (SELECT 2 LIMIT 0)
UNION SELECT '1 = NULL', (SELECT 1 LIMIT 0) = (SELECT NULL LIMIT 0);

What do you think? Are all empty sets created identical?
MySQL says no.

+----------+--------+
| equality | result |
+----------+--------+
| 1 = 1    |      1 |
| 1 = 2    |      0 |
| 1 = NULL |   NULL |
+----------+--------+