I thought monotonic meant that it only increased or decreased.
Well--Bean said that monotonic = not increasing, or not decreasing . (I added the boldface.) Not increasing means, I think, that something either stays the same or decreases; and the opposite for not decreasing. So it seems to me that her def. fits.

I looked at the site, and, while not coming anywhere near real comprehension, I did find it cool that they make a distinction for staying the same. If a sequence could stay the same or get smaller, they say it is "monotonically nonincreasing". If one could stay the same or get larger, they say it is "monotonically nondecreasing".