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I would like to ask if this system is Bounded Input Bounded Output stable :

$$y[n] = r^nx[n],\quad r\in \mathbb{R}$$

And why? I think this system is stable because

$$| x[n] | ≤ B,\quad B < \infty\Rightarrow |y[n] |=| r^nx[n]| \le |r^n| |x[n]|\le B < \infty$$

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The system is not BIBO stable because $r^n$ is not bounded for $|r|>1$.

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