效绵鼎 Example Uncountable Set Theorem:the real numbers R are NOT countable (they are“uncountable"). How do you prove such a statement? assume countable (so there exists bijection f) derive contradiction (some element not mapped to by f) o technique is called diagonalization (Cantor)Example Uncountable Set Theorem: the real numbers R are NOT countable (they are “uncountable”). ◼ How do you prove such a statement?  assume countable (so there exists bijection f)  derive contradiction (some element not mapped to by f)  technique is called diagonalization (Cantor)