14. Let $a, b, c \in \left(0, \frac{\pi}{2}\right)$, and satisfy the following equations: $\cos a = a$, $\sin (\cos b) = b$, $\cos (\sin c) = c$. Try to compare the sizes of $a, b, c$.
14. Proof by contradiction. Let $b \geqslant a$, since $y=\cos x$ is decreasing on $\left(0, \frac{\pi}{2}\right)$, and $0$ $\sin x . b=\sin (\cos b)\cos c \geqslant \cos a=a$ contradicts $c \leqslant a$, so it must be that $c>a$. Therefore, $c>a>b$.