- #1

mathmari

Gold Member

MHB

- 5,049

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Hey!

Let $v, w\in \mathbb{R} ^n$ and let $V, W\subseteq \mathbb{R} ^n$.

I want to show the following properties :

(Wondering)

Let $v, w\in \mathbb{R} ^n$ and let $V, W\subseteq \mathbb{R} ^n$.

I want to show the following properties :

- $d(u.,w)=0\iff u=v$

- $d(V, W) =0\iff V\cap W\neq \emptyset$

- $d(u, w) =0\iff |u-w|=0\iff u-w=0\iff u=w$

Or do we have to do more steps?

$$$$

- $d(V, W) =0\iff \min \{d(v, w) \} =0$ this means that there exists $v$ and $w$ such that $d(v, w) =0$ and from the previous one it follows that $v=w$ which means that the intersection is non empty.

Is that correct?

(Wondering)

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