I'm not quite sure how do I show this / find a counter example. Assume '=' refers to \in (set notation). Statement: If f(n) = o(n^c), then there...

I'm not quite sure how do I show this / find a counter example.

Assume '=' refers to in (set notation).

Statement: If f(n) = o(n^c), then there exists k > 0 such that f(n) = O(n^(c-k)), where c > 0.

I feel that this is false, and a counter example would be a function f(n) smaller than n^c but larger than n^(c-k).