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Math Help - Triangle inequality for R^n

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    Triangle inequality for R^n

    How would I show the triangle inequality for \mathbb{R}^{n} ?

    The only thing I can think of is induction and thinking about it, it doesnt make sense that the triangle inequality in \mathbb{R}^n depends on the triangle inequality in \mathbb{R}^2
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    Re: Triangle inequality for R^n

    Quote Originally Posted by Jame View Post
    How would I show the triangle inequality for \mathbb{R}^{n} ?

    The only thing I can think of is induction and thinking about it, it doesnt make sense that the triangle inequality in \mathbb{R}^n depends on the triangle inequality in \mathbb{R}^2
    Why would you say that?
    Is it not the case that \mathbb{R}^3=\mathbb{R}^2\times\mathbb{R}~?
    Thus \mathbb{R}^{n+1}=\mathbb{R}^n\times\mathbb{R}~.
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