An Intuitive Introduction to the p-adic Numbers
April 7, 2008
Bailey Hall 207
Refreshments will be served in Bailey 204 at 4 pm
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.
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