What are "complementary pair-wise comparable functions"?

Question

I got this term while studying periodic functions; my book writes:

If $f_1(x)$ & $f_2(x)$ are periodic functions with periods $T_1$ & $T_2$ 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 $f_1(x)$ & $f_2(x)$ 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.

score 1 · Answer 1 · edited Apr 15 '18 at 12:53

1

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 $cos(x)$.

edited Apr 15 '18 at 12:53

Tyrone

16,116

answered Apr 15 '18 at 12:35

Swastik

11

score -3 · Answer 2 · edited Mar 26 '16 at 18:56

-3

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 $x$.

edited Mar 26 '16 at 18:56

answered Mar 26 '16 at 18:52

Navneet

1

and what does it mean when you put "complementary" in there? – GEdgar Mar 26 '16 at 18:55
This interpretation doesn't seem to make much sense in the context of the question. – Eric Wofsey Mar 26 '16 at 19:27

What are "complementary pair-wise comparable functions"?

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