效绵 Example Uncountable Set ■Proof: suppose R is countable list R according to the bijection f: f(n) set x 0.a azaga4... 13.14159. where digit a#ith digit after decimal 25.55555.. point of f(i)(not 0,9) e.g.×=0.2312. 30.12345.. x cannot be in the list! 40.50000..Example Uncountable Set ◼ Proof:  suppose R is countable  list R according to the bijection f: n f(n) _ 1 3.14159… 2 5.55555… 3 0.12345… 4 0.50000… … set x = 0.a1a2a3a4… where digit ai ≠ i th digit after decimal point of f(i) (not 0, 9) e.g. x = 0.2312… x cannot be in the list!