In this note we show that all sets that are neither finite nor too dense are non-trivial to test in the sense that, for every \epsilon>0, distinguishing between strings in the set and strings that are \epsilon-far from the set requires \Omega(1/\epsilon) queries.
Specifically, we show that if, for infinitely many n's, the set contains at least one n-bit long string and at most 2^{n-\Omega(n)} many n-bit strings, then it is non-trivial to test.