Let f be a nondecreasing, but not necessarily continuous, mapping of the closed interval [0,1] into itself. Then f has a fixed point
, i.e., there is some x in [0,1] such that f(x)=x.
(Just to avoid any misunderstanding, [0,1] is the set of all real numbers between 0 and 1, with both 0 and 1 also included.)
(In reply to re: No Subject
Whoops, in all cases that I used (1/2)^n I should have used (1/2)^(n+1)
so if f(x)=1 for all x then the sequence should be 0, 1/2, 3/4, 7/8,...
Posted by Joel
on 2006-11-17 20:45:20