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Monotonic, Upper bound and lower bound
Given any sequence {an} we have the following terminology:
1. We call or denote the sequence increasing if an < an+1 for every n.
2. We call or denote the sequence decreasing if an > an+1 for every n.
3. If {an} is an increasing sequence or {an} is a decreasing sequence we denote it monotonic.
4. If there exists a number m like m ≤ an 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 an ≤ 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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