Math and science::Analysis::Tao::05. The real numbers

A sequence  $(a_n{)}_{n=1}^{\mathrm{\infty }}$ 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  $(a_n{)}_{n=1}^{\mathrm{\infty }}$ 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.)