৪৯তম বিসিএস ⎯ ফলিত গণিত [৫৬১]

One of the four defining properties of a metric is the triangle inequality. Linearity, differentiability, and continuity are not required.

This is just a scaled version of the discrete metric (using 2 instead of 1). Scaling by a positive constant preserves metric properties and yields the same topology, so it’s equivalent to the discrete metric.

A metric space is defined as a set X with a metric d that measures distance between elements.

• R,N are unbounded.

• [0,1] is bounded since all distances are ≤1.

Identity of indiscernibles means d(x, y)=0  ⟺  x=y.

This is the maximum (Chebyshev) metric.

 Completeness = all Cauchy sequences converge in the space.

 Each term is smaller than the previous → decreasing.

Exponentially increasing → goes to infinity → unbounded.