Metric
Concept history
A revision trail for this concept page.
Revision 4557
9/11/2026, 7:16:42 PM · Ancient Tree
Added exercise "Seconde inégalité triangulaire"
linked exercisesThe discrete metric, Distance carréeThe discrete metric, Distance carrée, Seconde inégalité triangulaire
Revision 4366
9/9/2026, 5:08:43 PM · Ancient Tree
Added exercise "Distance carrée"
linked exercisesThe discrete metricThe discrete metric, Distance carrée
Revision 930
8/5/2026, 7:21:34 AM · Sequoia
Concept edited
This older revision predates detailed metadata tracking.
Revision 901
8/4/2026, 2:46:42 PM · Ancient Tree
Concept edited
This older revision predates detailed metadata tracking.
Revision 899
8/4/2026, 2:38:23 PM · Ancient Tree
Concept marked usable
This older revision predates detailed metadata tracking.
Revision 898
8/4/2026, 2:38:21 PM · Ancient Tree
Concept edited
Compare with revision 5459 changed lines
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A metric on a set $X$ is a function $d:X\times X$ verifying...1
A metric on a [[Set|set]] $X$ is a [[Function|function]] $d:X\times X \rightarrow \R_{+}$ such that, for all $x,y,z\in X$: 2
1. Separation: $d(x,y)=0 \Leftrightarrow x=y$3
2. Symmetry: $d(x,y)=d(y,x)$4
3. Triangle inequality: $d(x,z)\leq d(x,y)+d(y,z)$5
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##### Remarks7
- The pair $(X,d)$ is then called a [[Metric space|metric space]].8
- $d(x,y)$ is called distance between $x$ and $y$.Revision 545
7/21/2026, 8:02:59 PM · Ancient Tree
Concept created
Recorded titleMetric
Recorded typeDefinition
A metric on a set $X$ is a function $d:X\times X$ verifying...