Exercise · ZW-METRIC-SPACE-002 · ★☆☆ Basic
With the taxicab distance \(d_1(P,Q)=|p_1-q_1|+|p_2-q_2|\), what is \(d_1((1,2),(4,6))\)?
Choose one option.
Show answer
- D. 7
Explanation
Add the absolute differences: \(3+4=7\). The value 5 would be the Euclidean distance.
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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