Math Problem Statement
is this proof good? \begin{proposition} Let $X$ be a normed vector space. Prove that $|x|-|y| \leq|x-y|$. \end{proposition} \begin{proof} We prove the reverse triangle inequality. Start with
By the triangle inequality, which states that $|x+y| \leq |x| + |y|$, we have
Thus, $|x|-|y| \leq|x-y|$. \end{proof}
Solution
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Math Problem Analysis
Mathematical Concepts
Normed Vector Spaces
Inequalities
Formulas
Triangle Inequality: $\|a + b\| \leq \|a\| + \|b\|$
Theorems
Reverse Triangle Inequality
Suitable Grade Level
Undergraduate
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