Monotonic/monotone vs. monotonous
At a physics conference I attended last week in Berlin, I came across yet another example of tricky distinctions to master. Several speakers confused the words monotonic or monotone with monotonous. While these words can be used interchangeably in some situations, only monotonic and monotone are correct in a mathematical context.
The Oxford online dictionary gives the following meaning for monotonous:
never changing and therefore boring
as well the synonyms dull and repetitious. Although you may also consider a monotonic function to be boring, this is not what you usually want to express in discussing your results. Instead, monotonic has a specific mathematical meaning. For example, the picture above shows a function that is monotonic (non-decreasing in this case).
The fact that monotonic/monotone and monotonous translate to the same German word (monoton) does not exactly help. In particular, it is crucial to choose the correct translation from the dictionary for your context. For example, entering monoton into the popular online dictionary leo.org produces monotonous, monotone, and monotonic (among other choices), with monotone and monotonic being clearly marked as mathematical expressions.