The set can be thought of as the set of infinite bit-strings.
Use the Cantor Diagonal argument to show that the set is not countable.
But can be mapped injectively into [0,1].
If you are allowed to accept the Continuum Hypothesis then you are done.
hello there, thanks for reading!
I need to prove that the cardinal number of {0,1}^N is the cardinality of the continuum, c.
{0,1)^N is that set {f(x) | f:{0,1} --> N}, i.e., all the functions from the set {0,1} to Natural numbers.
The thing is, I have never learned of sets and cardinal numbers, and the lecturer mentioned briefly what a cardinal number is - so I have no idea how to approach this kind of problem.
Help? Please? Pretty please?
Thanks!