The difference between P-adic ultrametric and Ultrametric
P-adic ultrametric is also noun with the meaning: the ultrametric with prime number p as parameter defined as d_p (x, y) = |x - y|_p.
Ultrametric is also adjective with the meaning: describing a metric whose triangle inequality has the stronger form d(x, z) \le \max\{d(x, y), d(y, z)\} .
check bellow for the other definitions of P-adic ultrametric and Ultrametric
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P-adic ultrametric as a noun (number theory):
The ultrametric with prime number p as parameter defined as d_p (x, y) = |x - y|_p ; i.e., such that the distance between two rational numbers is equal to the p-adic absolute value of the difference between those two numbers.
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Ultrametric as an adjective (mathematics):
Describing a metric whose triangle inequality has the stronger form d(x, z) \le \max\{d(x, y), d(y, z)\} .