A Example Uncountable Set Proof o suppose R is countable o list r according to the bijection f: set X=0. a1a2a3a4 13.14159 where digit a; t ith digit after decimal 25.55555 point of f((not 0, 9) eg.x=02312. 30.12345 x cannot be in the list 40.50000Example 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!