Algebra of cardinality



Cardinality of cartesian product

What about the cardinality of Cartesian products? So if we have sets:



We can have the Cartesian product set:


We can see that:


Cardinality of union and intersection

\(|A\lor B| = |A|+|B|-|A\land B|\)

Cardinality of powerset


Cardinality of complement

\(|a \setminus b|=|a|-|a\land b|\)

Cardinality of even/odd natural numbers

What about the cardinality of even numbers? Well, we can define a bijective function between each:


Similarly for odd numbers:


So these both have cardinality \(\aleph_0\).