I'm trying to get better understanding of binary operations, and I came across this problem: namely on one online discussions I saw that set intersection as binary operation doesn't have a unit, however I think it has:
The set intersection operation for any set universe $U$ is defined on the $\mathcal P(U) \times \mathcal P(U)$ set. From the definition of unit for binary operation, wouldn't it be true that the $U$ set is the unit of this operation. Any set in $PU$ intersected with $U$ will give back the set, and it works in both directions.
Am I doing something wrong, or the discussion on that place was wrong?