A sequence $$(a_n)_{n=1}^{\infty}$$ is said to be bounded away from zero iff there exists a rational $$c > 0$$ such that [...] for all integers $$k \ge 1$$.
A sequence  $$(a_n)_{n=1}^{\infty}$$ is said to be positively bounded away from zero iff there exists a rational $$c > 0$$ such that [...] for all integers $$k \ge 1$$. (In other words, the sequence is comprised entirely of positive rationals.)
A sequence  $$(a_n)_{n=1}^{\infty}$$ is said to be negatively bounded away from zero iff there exists a rational $$c > 0$$ such that [...] for all integers $$k \ge 1$$. (In other words, the sequence is comprised entirely of negative rationals.)