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

Sequences bounded away from zero

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.)