1. The problem statement, all variables and given/known data x_n=1/sqrt(n) Prove that lim x_n = 0 as n approaches infinity 2. Relevant equations E > 0 3. The attempt at a solution There is a natural number N such that N>1/sqrt(E). There is also a number n>N>1/sqrt(E) <==> sqrt(n)>1/sqrt(sqrt(E)) ==> E>sqrt(sqrt(E))>1/sqrt(n). If this last inequality is correct, I can prove the limit in question. But it can't be, because E<sqrt(sqrt(E)) if 0<E<1. So, what should I do instead?