Interesting properties of CROSS JOIN - SQL

Compare these with the "interesting properties of JOIN", CROSS JOIN is associative but not commutative. Unlike JOIN and NATURAL JOIN, CROSS JOIN is not idempotent. Let t be any table and let n be its cardinality. Then t CROSS JOIN t has twice as many columns as t and n2 rows. Also unlike JOIN, CROSS JOIN has no identity value. If t is a table, there is no table t0 such that t CROSS JOIN t0 = t. That's because t0 would be required to have no columns and exactly one row, but SQL doesn't recognize the existence of tables with no columns.