Originally Posted by
alexandrabel90 may i know why "if the function f on a closed bounded interval [a,b] is unbounded then there exist a seq x_n in [a,b] st l f(x_n)l > n for all n"
i was trying to list a few examples to show why this is true but i do not get it.
it seems to be that the function f on a closed bounded interval [a,b] can be bounded and yet there exist a seq x_n in [a,b] st l f(x_n)l > n for all n.
this was my working:
assuming that the function is from [0,10] where the range is [ 20,30] which means that f(x)= 20+x
then taking the even seq, f(x_1)= 22, f(x_2)=24... where 22>1, 24> 2.. hence
f(x_n) > n for all n, where in this case, the function is bounded.
may i know what mistake i have made?
thank you!