Suppose $x[n] = e^{j\omega n }$. I've seen following statement many times in the different sources:

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> For the discrete-time sinusoidal signal $x[n]$, as $\omega$ increases from $\omega = 0$ toward $\omega = \pi$, $x[n]$ oscillates progressively more rapidly. However, as $\omega$ increases from $\omega = \pi$ to $\omega = 2\pi$, the oscillations become slower.
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I think it means that if we increase $\omega = 0$ toward $\omega = \pi$, fundumental frequency of $x[n]$ should increase. If we set $\omega = \frac{\pi}{3}$ then $$\frac{\omega}{2\pi} = \frac{\pi /3 }{2\pi} = \frac{1}{6} = \frac{m}{N} \implies f\_0 = \frac{w}{m} = \frac{\pi}{3}$$
and if $\omega = \frac{5\pi}{13}$ then $$\frac{\omega}{2\pi} = \frac{5\pi /13 }{2\pi} = \frac{5}{26} = \frac{m}{N} \implies f\_0 = \frac{w}{m} =\frac{\pi}{13}$$
So we have increased $\omega$ but the fundamental frequency has been decreased.

So what's wrong here? Is my understanding about the aforementioned statement wrong? If so, what happens exactly to the fundamental frequency as we change $\omega$?