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saxen
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Denote by d(x,A) = inf |x-y|,y [itex]\in[/itex] A, the distance between a point x [itex]\in[/itex] R^n and a set A [itex]\subseteq[/itex] R^n. Show
|d(x,A)-d(z,A)| [itex]\leq[/itex] |x-z|
In particular, x → d(x,A) is continuous
I have no idea on how to prove this. I drew a picture and the result seemed intuitive but I don't know how to prove it mathematically.
Appriciate any help!
Homework Statement
Denote by d(x,A) = inf |x-y|,y [itex]\in[/itex] A, the distance between a point x [itex]\in[/itex] R^n and a set A [itex]\subseteq[/itex] R^n. Show
|d(x,A)-d(z,A)| [itex]\leq[/itex] |x-z|
In particular, x → d(x,A) is continuous
Homework Equations
The Attempt at a Solution
I have no idea on how to prove this. I drew a picture and the result seemed intuitive but I don't know how to prove it mathematically.
Appriciate any help!