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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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FredJeffries@gmail.com

Posts: 877
Registered: 11/29/07
Re: What is the intuitive meaning of "non-Archimedean" for a valued field?
Posted: May 14, 2013 10:37 PM
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On May 13, 6:32 pm, mike3 <mike4...@yahoo.com> wrote:
>
> How can one intuitively grasp the geometry of a non-
> Archimedean valued field



All triangles are isosceles and the unequal side is the shortest one.
Two discs cannot partially intersect.
Every point of a disc may be regarded as its center.

Think of different orders of magnitudes: from across the room, two
different molecules in a glass are pretty much the same distance from
you. But you and the glass are pretty much the same distance from the
stop sign down the street.

Two different people in new york are pretty much the same distance
from a person in Chicago but all three are pretty much the same
distance from a rock on the moon. Them moon, the three people, the
stop sign and the glass are all pretty much the same distance from the
rings of Saturn...


https://www.colby.edu/math/faculty/Faculty_files/hollydir/Holly01.pdf

From Alain Robert "A Course in p-adic Analysis" p. vi
"Intuitively, this absolute value plays the role of an order of
magnitude. If x has a magnitude greater than 1, one cannot reach from
0 it by taking a finite number of unit steps (one cannot walk or drive
to a neighboring galaxy!)"



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