Hey all, I have been thinking about this question and am having trouble ruling out one of the answer choices. Help on it is much appreciated!

Which of the following sets has the greatest cardinality?

A) R

B) The set of all functions from Z to Z

C) The set of all functions from R to {0,1}

D) The set of all finite subsets of R

E) The set of all polynomials with coefficients in R

Ok, so R had cardinality C. I also know the set of all sequences of real numbers has cardinality C (IE set of all functions N->R), so the choice E) has cardinality C. Since each finite subset of R can be a polynomial with coefficients of R, I think D) has cardinality C as well.

How do I rule out choice B? (The answer is C)