Strict Monotonicity

As discussed before, if said function or sequence keeps only giving smaller and smaller or larger and larger outputs, but never the same as the previous output element, then this function is strictly monotone.

In the case it keeps growing, it's strictly increasing
Similarly, in the case it keeps getting lower and lower, it's strictly decreasing.

Now, pause for a second and think about something.
Hmmm.. strict monotonicity means that the next element will always be larger or smaller. So, no two outputs will be the same.

Sounds familiar, doesn't it?
Indeed:Warning: More often than not, the vice-versa is also true, but it can not and should not be taken for granted. Strict monotonicity does not necessarily imply injectivity.

Done!
Take a minute to take a deep breath and relax your eyes a bit.

Next -> Convergence