Here is where the idea of halt was taught in the class, and kinda really shook the world of me. To think that halt, something that we have an idea for, cannot be implemented because it'd create a paradox!
Finally, this brings up to the idea of countability. Sets have bigger sets than some other "sets", and things are only countable if a set can be mapped to natural numbers. In this manner, the halting problem is an extension of this problem.
The size of the set of solvable problems are less than the size of the set of all problems, and the halting problem just happens to lie on the other side.
