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**Question 1**

**Prove that if [itex](V, \|\cdot\|)[/itex] is a normed vector space, then**

[tex] \left| \|x\| - \|y\| \right| \leq \|x-y\|[/tex]

**for every [itex]x,y \in V[/itex]. Then deduce that the norm is a continuous function from [itex]V[/itex] to [itex]\mathbb{R}[/itex]**.