Is there an error in the following proof?
Proposition: $\forall r \in {N} ; r \neq 1$ , then $\exists$ $n \in {Z}$ such that $$2^{1/n} < r$$
Proof: Let $n$ be any integer with $$n > 1/ log_2 r$$ Then $$1/n < log_2r$$ Hnece $$2^{1/n} < 2^{log_2r} = r$$