Which of the following is a requirement for a metric space?
- Distance from a point to itself must be non-zero
- Triangle inequality must hold
- Distance must be infinite
- None of these
Explanation
A metric space is a set with a distance function (metric) that meets three properties:
1. Non-negativity: Distances are always non-negative.
2. Symmetry: Distance from A to B equals distance from B to A.
3. Triangle Inequality: For any points A, B, and C, the distance from A to C is less than or equal to the sum of the distances from A to B and B to C.
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