I would like to make sure my answer #1 is correct. About #2, I thought I would use (0, 1] or [0, 1] to prove the bijection. I used the Schrder-Bernstein theorem, but it is not for bijection. Could you tell me some advice?

Thanks,

(1) Find the cardinality of the set S={x | sinx=1}. Prove your claim by finding a bijection.

(2) Find the cardinality of the set (0; 1). Prove your claim by finding a bijection.

My answer:

2 f : (0, 1) - [0, 1], f(n) = n f is one-to-one: If f(m) = f(n), then by definition of f m = n If |A|