Exercise · ZW-METRIC-SPACE-003 · ★☆☆ Basic
With the max distance \(d_\infty(P,Q)=\max\{|p_1-q_1|,|p_2-q_2|\}\), what is \(d_\infty((1,2),(4,6))\)?
Choose one option.
Show answer
- A. 4
Explanation
The differences are \(3\) and \(4\); the maximum is \(4\).
Review the concept: Metric space
A metric space is a set \(X\) together with a distance \(d\) between its points: a nonnegative number for each pair, symmetric, zero only between a point and itself, and satisfying the triangle inequality.
\[\begin{aligned}d(x,y)&=0\iff x=y,\qquad d(x,y)=d(y,x),\\ d(x,z)&\le d(x,y)+d(y,z)\end{aligned}\]
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