p-adic numbers
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Liu
Dec 17, 2009, 9:16:16 AM12/17/09
to maths learning
p-adic numbers are very funny. It seems quite strange because of the
non-Archimedean metric. Two numbers are close only when their
difference is divisible by a large power of a fixed prime p. But the
surprising theorem of Ostrowski shows that all nontrivial norms on Q
can divide into two kinds. One is the normal norm, the other generates
p-adic numbers.
non-Archimedean metric. Two numbers are close only when their
difference is divisible by a large power of a fixed prime p. But the
surprising theorem of Ostrowski shows that all nontrivial norms on Q
can divide into two kinds. One is the normal norm, the other generates
p-adic numbers.
Wiki has a page talking about p-adics, which start form its general
representation.
http://en.wikipedia.org/wiki/P-adic_number
This representation comes from a theorem, which is in page two of Neal
Koblitz’s book. More materials are also introduced in this book,
including the arithmetic of this new number system.
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