Prove Metric Space: d_p Not Metric when p < 1

[complexnumber]

Homework Statement

Let X = \mathbb{R}^n be equipped with the metric
<br /> d_p(\boldsymbol{x}, \boldsymbol{y}) := \left[ \sum^n_{i=1} |x_i<br /> - y_i|^p \right]^{\frac{1}{p}}, p \geq 1<br />

Homework Equations

Show that if p &lt; 1 then d_p is not a metric.

The Attempt at a Solution

I don't know what approach I should take. The textbooks have proofs showing that when p \geq 1 the function d_p is a metric but only uses p in the equation \displaystyle \frac{1}{p} + \frac{1}{q} = 1. Can someone give me a hint where I should start?

 

[Hurkyl]

Trying specific examples is often useful.

 

[complexnumber]

I still can't figure out. Can you give me more hint?