Hi(adsbygoogle = window.adsbygoogle || []).push({});

I have another question in the field of analysis.

[tex]Y \subseteq \mathbb{R}^n[/tex]

I'm suppose to show that if [tex]x \in \mathbb{R}^n[/tex], then the set

[tex]\{ || x - y || \ y \in Y \}[/tex]

has an infimum, such that

[tex]f(x) = \mathrm{inf} \{ || x - y || \ y \in Y \}[/tex]

I know that I'm suppose to show that the infimum is the shortest distance between x and y. But how I proceed from there?

Where [tex]f: \mathbb{R}^n \rightarrow \mathbb{R}[/tex].

Sincerely Yours

Mathboy20

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Infimum of a metric space

**Physics Forums | Science Articles, Homework Help, Discussion**