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Math and science::Topology

Metric space

Metric

A metric \( d \) on a set \( X \) is a function [ \( d : \text{what} \to \text{ to what?} \)] with the following three properties:

What is this called?
\( d(x, y) = 0 \iff x = y, \text{ for all } x, y \in X \)
Triangle inequality
[...]
Symmetry
\( d(x, y) = d(y, x), \text{ for all } x, y \in X \)

A metric space is a set together with a metric on it, or more formally, a pair \( (X, d) \) where \( X \) is a set and \( d \) is a metric on \( X \).