Monotonic, upper bound and lower bound, Mathematics

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Monotonic, Upper bound and lower bound

Given any sequence {a_n} we have the following terminology:

1. We call or denote the sequence increasing if a_n < a_n+1 for every n.

2. We call or denote the sequence decreasing if a_n > a_n+1 for every n.

3. If {a_n} is an increasing sequence or {a_n} is a decreasing sequence we denote it monotonic.

4. If there exists a number m like m ≤ a_n for each n we say the sequence is bounded below. Occasionally the number m is called a lower bound for the sequence.

5. If there exists a number M like a_n ≤ M for every n we say the sequence is bounded above. Occasionally the number M is called an upper bound for the sequence.

6. If the sequence is both of the bounded below and bounded above we denote the sequence bounded.

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