Countability!

The lecture this week left me surprised. I couldn't believe that the size or natural numbers was equal to the size of even natural numbers.

I learned that when given two sets, for example X and Y, if there exists a well defined function f: X→Y that is 1-1 and onto, the the size of X is equal to the size of Y. This can be used compare the sizes of sets with infinity many elements. The only issue is finding f: X→Y.

I also learned that any set that is less than or equal to the size of natural numbers qualifies as countable. What also surprised me was that there are countable infinitely many python functions that can be written because each and every python function can be turned into a unique natural number. This also surprised Kevin, which he wrote on his blog.