# Proper term for non-linear proportionality

I want to express the simple idea that two functions f and g are related in the following way:

$$f(x) > f(y) \implies g(x) > g(y)$$

Or the inverse relation:

$$f(x) > f(y) \implies g(x) < g(y)$$

I was going to use the term "proportional" or "inversely proportional", but I understand that in mathematics that implies a linear (or inverse linear) relationship, which is not my case. Is there a better term to express this than something like "$f(x)$ increases as $g(x)$ increases/decreases"?

• I don't know a standard term, but if I were to make one up, I'd choose something like "$f$ and $g$ increase (in)coherently". – user228113 Sep 5 '17 at 15:12
• Isn't this the problem that big and little "oh" notation are meant to address? – Xander Henderson Sep 5 '17 at 15:39
• @XanderHenderson Mmm, well I was thinking more of a term, but in any case, I don't really want to say either $f \in \mathcal{O}(g)$ or $g \in \mathcal{O}(f)$, since none of them actually "bounds" the other... also I couldn't express the inverse relationship like that, I think. – jdehesa Sep 5 '17 at 16:00
• If we're making up terms, "$f$ and $g$ are co-ordered". – Eric Towers Sep 5 '17 at 16:05
• This has nothing to do with proportionality, nor with order of magnitudes, just with order. This question is a linguistic and semantic challenge indeed. – Christian Blatter Sep 5 '17 at 16:13