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@@ -88,8 +88,8 @@ |
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\item Dreicksungleichung: |
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\begin{align*} |
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\Vert x + y \Vert \quad &= \quad d(x + y, 0) \\ |
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&\stackrel{\text{E1}}{=} \quad d(y, -x) \\ |
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&\stackrel{d \text{ Metrik}}= \quad d(-x, y) \\ |
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&= \quad d(y - (-x), 0) \\ |
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&\stackrel{\text{E1}}{=} \quad d(-x, y) \\ |
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&\stackrel{d \text{ Metrik}}\le \quad d(-x, 0) + d(0, y) \\ |
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&\stackrel{\text{E2}}{=} \quad d(x, 0) + d(y, 0) \\ |
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&= \quad \Vert x \Vert_d + \Vert y \Vert_d |
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