The distance between two points A and B on a line is the length of the line segment that joins points A and B.
The concept of distance is also used to refer to the amplitude of an interval on a number line
Notation
The distance between the points A and B is written as: d(A, B) and is read as “the distance from A to B.”
Properties
For all x, y, z elements of \(\mathbb{R}\), we have :
- d(x, y) = 0 ↔ x = y (separation axiom)
- d(x, y) = d(y, x) (symmetry)
- d(x, y) ≤ d(x, z) + d(z, y) (triangle inequality)
- d(x, y) = |x − y|.