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Topic: What is the intuitive meaning of "non-Archimedean" for a valued field?
Replies: 11   Last Post: May 15, 2013 4:29 PM

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Brian Q. Hutchings

Posts: 6,213
Registered: 12/6/04
archmimedean valuation is infinity-adic numbering
Posted: May 14, 2013 10:38 PM
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as an old aerospace engineer once said,
"my congruence surds are not p-adic numbers, but
that's what most mathematicians mistook them, for;"
although he didn't say it,
the canonical p-adic numbers are actually not prime-
based, but 10-adics:
subtract a larger number from a smaller,
a la backwards on the odometer.

he also said that
they are not useful for valuations, but
only for eliminating classes of congruences,
mod p, a prime.



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