## An Intuitive Introduction to the |

**Karl Zimmermann**

Union College

April 7, 2008

4:15 pm

Bailey Hall 207

Refreshments will be served in Bailey 204 at 4 pm

For each primep, there is a number system called thep-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, thep-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 thep-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 + 2 ^{2}+ 2^{3}+ 2^{4 }...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.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Mon Jul 23 03:39:42 EDT 2018 |