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 \(\varOmega (1/\epsilon )\) queries. Specifically, we show that if, for infinitely many n’s, the set contains at least one n-bit long string and at most \(2^{n-\varOmega (n)}\) many n-bit strings, then it is non-trivial to test.