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An Intuitive Introduction to the p-adic Numbers

by

Karl Zimmermann
Union College

April 7, 2008
4:15 pm
Bailey Hall 207

Refreshments will be served in Bailey 204 at 4 pm


Abstract:

For each prime p, there is a number system called the p-adic numbers. These systems, first introduced by Kurt Hensel at the end of the 19th century, play a central role in various areas of number theory and arithmetic geometry.   Like the real numbers, the p-adic numbers contain the rationals, and while there are many other similarities, much is different.   In this talk, I'll give an intuitive introduction to the p-adic numbers, highlighting similarities with the reals, but focusing on some differences.  For example, we'll begin by making sense of the equation                
-1 = 1 + 2 + 22 + 23 + 24 ...

which, in the p-adic numbers, really is an equation.


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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