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

Bounded sequences

Let \( M >0 \) be a rational. 

A finite sequence (of rationals, but equally applies to reals) \( a_1, a_2, a_3, ..., a_n \) is bounded by M iff [...] for all \( 1 \ge i \ge n  \).

An infinite sequence \( (a_n)_{n=1}^{\infty} \) is bounded by M iff [...] for all \( i \ge 1 \).

A sequence is said to be bounded iff it is bounded by some \( M \ge 0 \).