Seven different proofs for
Cong-Cong Xing · Journal of computing sciences in colleges · 2016
Solving one problem in different ways has its established benefits in developing and enhancing students' problem-solving abilities at all levels of school. But this teaching strategy does not seem to have received sufficient attentions and been accordingly practiced in college level computer science classrooms. We in this paper present seven different ways of proving the cardinality of power set |P(A)|=2n for any set A with |A|=n, and then discuss their main ideas, complexity (or simplicity), and internal connections. Our goal is to advocate and contribute to this teaching strategy.