Set S is a set consisting of all string of one or more a or b such as a, b, ab, ba, abb, bba... and how to prove set S is a infinity set.I have tried proving set S as one to one corresponding to natural number set in binary form. like a = 0, b = 1. However, I am stuck in proving it since there are more than one 1, 01 = 1, same as other numbers. 
How to prove a set has infinite cardinality?
proof techniques;sets