22 - Monotonic Sequences

Monotonic Increasing / Decreasing

Let $(a_n)$ be a real sequence

1. Monotonic Increasing / Monotone Increasing / Increasing:

$$a_n\le a_{n+1}\text{ for all }n$$

2. Monotonic Decreasing / Monotone Decreasing / Decreasing

$$a_n\ge a_{n+1}\text{ for all }n$$

3. Monotonic / Monotone

$$\text{Either increasing or decreasing}$$

Strictly Increasing / Decreasing

Let $(a_n)$ be a real sequence
4) Strictly Increasing:

$$a_n<a_{n+1}\text{ for all }n$$

5. Strictly Decreasing

$$a_n>a_{n+1}\text{ for all }n$$

Constant sequence is both increasing and decreasing!