Monotonicity

Let's try to understand the name first. Mono-tone. Only of one tone. In mathematics, this will mean that functions and sequences that have this property only "behave in one way".

What does this mean, exactly?

This means that as we keep on counting for a sequence or taking bigger and bigger or smaller and smaller inputs for a function, the next element of the output set will either be larger or equal to, or smaller or equal to than the previous.

If the next output element is always larger or equal to the previous, this function is monotone, more specifically monotonically increasing. Meaning, its outputs will either stay the same at some points or just get bigger and bigger.

Similarly, if the next output is always less than or equal to the previous, this function is also monotone, specifically monotonically decreasing. This means that its outputs will either stay the same at some points or just get smaller and smaller.

In the cases that it never stays the same, we have:
Strict Monotonicity