Definition:
A sequence or function is monotonically increasing if it never decreases as you move from left to right (or from one term to the next). In other words, each value is greater than or equal to the previous value.
Mathematically, for a sequence $a_1, a_2, a_3, \ldots, a_n$, it’s monotonically increasing if $a_1 \le a_2 \le a_3 \le \ldots \le a_n$.
Example:
Your daily step count over a week:
- Monday: 5,000 steps
- Tuesday: 5,000 steps
- Wednesday: 6,200 steps
- Thursday: 6,200 steps
- Friday: 7,800 steps
- Saturday: 8,500 steps
- Sunday: 8,500 steps
This sequence is monotonically increasing because each day’s count is $\ge$ the previous day’s count.