Week 10

This week, new and different concepts were introduced throughout lectures. I never really thought about the limits of computer science seeing as it's regarded as still a new and expanding field. So when Danny introduced functions that could not be programmed, I was quite intrigued. I understand that the halt function cannot work on all functions (in the case of the function calling halt within itself, EX navel gaze), and many other functions that would extend to halt, also cannot be implemented because halt cannot be implemented.
Another new concept introduced this week was the concept of different sized infinite sets. I find the concept of infinite sets and the definition of countable to be a tricky and un-natural concept. For finite sets, the definition of one-to-one and onto make sense, however, I find it hard to visualize this concept with infinite sets. For example, the definition of one-to-one and onto is satisfied with the sets of natural numbers, even natural numbers, and odd natural numbers(compared to natural numbers). Therefore, the  set of natural numbers has the same size as the set of even natural numbers AND the same size as the odd natural numbers, although the set of natural numbers contains BOTH the even and odd natural numbers.