slog for week of Nov. 17

• What's new?

          This week's a short week, but stuff for this week is totally new and super difficult for me I think. And honestly, I'm very confused about what we've learnt in this week. A totally new concept - computable and non-computable, had been introduced to us, through the example function, halt. 

          Then we've learnt about finite sets. This part is more understandable i think, especially the concept of 1-1 and onto cause they've been introduced in other math courses like MAT223 and MAT137(something related to other courses). Thus I can understand whynot 1-1 will result over-count and not onto result undercount. And we have the conclusion: every set which is smaller than natural number set is always countable. 

• Problem?

          1. I'm not quite well understand the halt function and navel_gaze function which were talked about on Wednesday's lecture. What makes them become non-computable function? And how I can distinguish a given function is computable or not?

          2. Friday's lecture, our prof said set of rational number has the same size to the set of  natural number. I'm questioning why?