1. The problem statement, all variables and given/known data Prove that the union of c sets of cardinality c has cardinality c. 2. Relevant equations 3. The attempt at a solution Well, I could look for a one-to-one and onto function... maybe mapping the union of c intervaks to the reals, or something? I know how to demonstrate that a countable union of countable sets is countable, by showing how to label them. I'm having a hard time with this one, though.