What are "complementary pair-wise comparable functions"? I got this term while studying periodic functions; my book writes:


  If $f_1(x)$ &amp; $f_2(x)$ are periodic functions with periods $T_1$ &amp; $T_2$ respectively, then we have $h(x) = f_1(x) + f_2(x)$ has period, as $\dfrac{1}{2} \text{L.C.M. of }\; \{T_1 ,T_2\}$, if $f_1(x)$ &amp; $f_2(x)$ are complementary pair-wise comparable functions.


Don't know how the author deduced the rule. But my main question is what do this "complementary, pair-wise, comparable function" mean?  I've googled this but it was in vain.
I think it means if you put $(π/2-x)$ in place of $x$ in one of the functions and get the second function, then they are called complementary. Like $sin(x)$ and $cos(x)$.
Consider a set of functions $F$. 

The set is pairwise comparable if, for any two functions $f(x)$ and $g(x)$ within the set $F$, we know that either: 

$f(x) \ge g(x)$ for any value of $x$, or 
$f(x) \le g(x)$ for any value of $x$.