Cartesian Product
The Cartesian product of two sets and , denoted as , is the set of ordered pairs with and .
In symbols,
Contents
Cartesian product of two sets
Let . What is ?
Referring to the definition, .
We can list the elements out:
Cartesian product of finite number of sets
Cartesian product of finite number of sets is similar to that of two sets. Instead of a formal definition, an example is given here.
Let . What is ?
Listing the elements out:
Cartesian power of set
From product of numbers we can define power of numbers. Similarly, from Cartesian product we can define Cartesian power.
which is all 3-tuples with real number as elements.
Cardinality of Cartesian product of set
We have where denotes the cardinality of the set .
Let . What is ?
Cardinality of Cartesian power of set
We have
Let . What is ?