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.