# Math Help - Triangle inequality for R^n

1. ## 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 $\mathbb{R}^2$

2. ## Re: Triangle inequality for R^n

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 $\mathbb{R}^{n+1}=\mathbb{R}^n\times\mathbb{R}~.$