Problem statement:
Let A be an uncountable set, B a countable subset of A, and C the complement of B in A. Prove that there exists a one-to-one correspondence between A and C.
My thoughts:
There's a bijection between A and A (the identity function). There's a bijection between C and C (the identity function). There's a bijection between B and $\mathbb{N}$. That's all I know.