Triangle inequality for R^n

**Jame** · September 16th 2011, 07:54 PM

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 $\mathbb{R}^2$

**Plato** · September 17th 2011, 02:32 AM

Originally Posted by Jame

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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