Hmmmmm

Last week we began talking about the halting function in Danny's section. We also talked about the size of sets, and how to count big sets like the rational numbers. He showed that the size of even numbers is the same as the size of natural numbers. It's not intuitive but I guess it makes sense from the definition. Hmmmmm

Hmmmm

We are learning about using big O notation for algorithms in class. It's mostly the same as our old proofs but we have to count how many steps a function takes. Then we started doing more big O proofs in class. They also seem like our old proofs, except the statements are much longer and there is a similar structure in most big O proofs. Finally we started learning about computability in Larry's class. I'm confused about what a well defined function is. Larry said a well defined function is a function we know what the output should be for every input. Or something like that. And he said that a computable function is a function we know how to get the output. The halting function is supposed to say whether a program or function halts, and he gave an example of a function that loops if the halting function says it halts, and stops if the halting function says it doesn't, so there is a contradiction. But if the halting function is well defined, what is the output supposed to be for this special function? I wish I understood this class better, like those people who always raise their hand and speak really loudly. Someone even took the time in lecture to explain to everyone where the number 42 comes from. That was very helpful, because I would have been confused about the code example otherwise.