diff --git a/sose2020/ana/uebungen/ana3.pdf b/sose2020/ana/uebungen/ana3.pdf index 4504704..f2a414f 100644 Binary files a/sose2020/ana/uebungen/ana3.pdf and b/sose2020/ana/uebungen/ana3.pdf differ diff --git a/sose2020/ana/uebungen/ana3.tex b/sose2020/ana/uebungen/ana3.tex index b76d123..3fc9d3d 100644 --- a/sose2020/ana/uebungen/ana3.tex +++ b/sose2020/ana/uebungen/ana3.tex @@ -88,8 +88,8 @@ \item Dreicksungleichung: \begin{align*} \Vert x + y \Vert \quad &= \quad d(x + y, 0) \\ - &\stackrel{\text{E1}}{=} \quad d(y, -x) \\ - &\stackrel{d \text{ Metrik}}= \quad d(-x, y) \\ + &= \quad d(y - (-x), 0) \\ + &\stackrel{\text{E1}}{=} \quad d(-x, y) \\ &\stackrel{d \text{ Metrik}}\le \quad d(-x, 0) + d(0, y) \\ &\stackrel{\text{E2}}{=} \quad d(x, 0) + d(y, 0) \\ &= \quad \Vert x \Vert_d + \Vert y \Vert_d