- #1
fireboy420
- 11
- 0
Any hint PLZ
[PLAIN]http://img151.imageshack.us/img151/1715/1111111111k.jpg [Broken]
Thank You
[PLAIN]http://img151.imageshack.us/img151/1715/1111111111k.jpg [Broken]
Thank You
Last edited by a moderator:
A metric space is a mathematical concept used to define the distance between two points in a given set. It is a generalization of the concept of distance in Euclidean geometry and is used in various branches of mathematics, including analysis and topology.
A metric space only defines the distance between points, while a normed space also includes the concept of magnitude or size of vectors. In other words, a metric space is a special case of a normed space where the norm is the distance function.
Some important properties of a metric space include the triangle inequality, which states that the distance between any two points in the space is always less than or equal to the sum of the distances between those points and a third point. Another important property is the symmetry property, which states that the distance between two points is the same regardless of the order in which the points are considered.
Metric spaces are used in various real-world applications, such as in GPS navigation systems, where the distance between different locations is calculated using the coordinates of those locations. They are also used in data analysis and machine learning algorithms, where the distance between data points is used to cluster or classify them.
Some common examples of metric spaces include the Euclidean space, which is the classic example of a metric space, as well as the discrete metric space, where the distance between any two points is either 0 or 1. Other examples include the taxicab metric space, where the distance between two points is the sum of the absolute differences in their coordinates, and the p-adic metric space, which is used in number theory and algebraic geometry.