1. The problem statement, all variables and given/known data Let S be infinite and, A a subset of S be finite. Prove that that the cardinality of S = the cardinality of S excluding the subset of A. 2. Relevant equations 3. The attempt at a solution We can write out the finite subset A as (x1, x2, ... xn) which can be put into a one to one correspondence with N. S is infinite so a bijection to N is not possible by definition. The cardinality of S excluding A is still uncountable but I don't see why they MUST have the same cardinality.