inf{a,bn :n e N} > (inf{an : n e N}) × (inf{b, : n € N}). (1) Can the inequality in (1) be strict? In other words, are there sequences (an)1 and (bn)-1 of non-negative real numbers such that inf{anbn : n e N} > (inf{an : n E N}) × (inf{bn : n E N})? Justify your answer.

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