Ultrametric
المؤلف:
المرجع الالكتروني للمعلوماتيه
المصدر:
www.almerja.com
الجزء والصفحة:
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30-7-2021
1901
Ultrametric
An ultrametric is a metric which satisfies the following strengthened version of the triangle inequality,
for all 
. At least two of 
, 
, and 
are the same.
Let 
be a set, and let 
(where N is the set of natural numbers) denote the collection of sequences of elements of 
(i.e., all the possible sequences 
, 
, 
, ...). For sequences 
, 
, let 
be the number of initial places where the sequences agree, i.e., 
, 
, ..., 
, but 
. Take 
if 
. Then defining 
gives an ultrametric.
The p-adic norm metric is another example of an ultrametric.
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