Query on the meaning of max notation

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When given, max{a,b}, where a and b are sequences of non negative terms What does this notation mean? I assumed it meant the largest value thats in both sequences however after further reading it asks me to sum this max which means that cant be right.

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Probably it means the sequence $c_n = \max\{a_n,b_n\}.$ It's the sequence of max's, not the max of sequences.