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**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!