Why is $L_0$ norm not convex? [closed]

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I have this confusion in understanding the convexity of the $L_0$ norm. Why is $L_0$ norm not convex?

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1 Answer

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$$\|\frac{1}{2}(1,0)+\frac{1}{2}(0,1)\|_0=2 > 1=\frac{1}{2}\|(1,0)\|_0+\frac{1}{2}\|(0,1)\|_0$$

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