# Cartesian product of omega tuples

1. Oct 19, 2011

### EV33

1. The problem statement, all variables and given/known data
So I am just trying to understand the concepts here.

My main question is what exactly is the cartesian product of an omega tuple?

2. Relevant equations

Given a set X, we define an ω-tuple of elements of X to be a function
x:N$\rightarrow$X

We denote x as
Let {A1,A2,...} be a family of sets

Let X be the union of of the sets in this family.

The book claims that the cartesian product of this indexed family of sets is denoted A1XA2....
and is defined to be the set of all ω-tuples (x1,x2,...) of elements of X such that xi is in Ai for each i, which is denoted by Xω.

3. The attempt at a solution

So is Xω=x? because that is what the book makes it sound like to me.

Also, the book tells me what the cartesian product of the indexed family is but it doesn't explain what the cartesian product of an omega tuple is. Can anyone explain what it is to me.