I'm working on a discrete math exercise and need support to help me learn.

Cantor's diagonal argument is a general method to proof that a set is uncountable infinite. We basically solve problems associated to real numbers represented in decimal notation (digits with a decimal point if apply). However, this method is more general that it.

Solve the following problem

Problem

Using the Cantor's diagonal method to prove that the following set is uncountable.

To get full credit you must write a rigorous proof including every part of the method.

The set of all functions$:N\to \{0,1\}$, i.e., all functions from the set of natural numbers $N$ to $\{0,1\}$.