Purchase Solution

# Cartesian product proof

Not what you're looking for?

I need help constructing a proof for the
Cartesian product of finitely many countable sets is countable.

##### Solution Summary

This is a proof regarding the Cartesian product of countable sets.

##### Solution Preview

First let's state the counting theorem:
"The Counting Theorem":
Let S be a set. The following are equivalent.
(i) S is either finite or a countably infinite set.
(ii) Either S = Null or there is a surjective map alpha: N ---> S.
(iii) There is an injective map beta: S ---> N.
If any of these three equivalent conditions hold, then we say
that S is a countable set.
This theorem has a ...

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.