MATC Mathematics Club
Lecture #107
Madison Area Technical College
Madison, Wisconsin
Professor Paul Zorn, St. Olaf College, MN and
President of the Mathematical Association of America
Abstract: Finite sets, like S = {a, e, i, o, u} and T = {a, b, c, d, ... z}, behave pretty much as anyone would expect. For example, it seems --- and is --- perfectly reasonable to say that T is "larger" than its proper subset S; indeed, T is genuinely "larger" than any proper subset. Infinite sets, by comparison, can behave quite counter-intuitively. The infinite set of all integers, for instance, is really no "larger" than the set of positive. The infinite set of real numbers, by contrast, is really (no pun intended) much, much larger than the set of integers. I'll explain how mathematicians have thought about these things, correctly or incorrectly, over the centuries, and point to some even more mysterious properties.
Biography: Paul Zorn is a professor of mathematics at Saint Olaf College and President of the MAA. Born and raised in India, Zorn moved to the U.S. to attend Washington University in Saint Louis, majoring in mathematics and English. He did his PhD, in several complex variables, at the University of Washington, Seattle, under the direction of Edgar Lee Stout. In 1981 he joined the faculty of St. Olaf, where he chaired the Department of Mathematics, Statistics, and Computer Science. He has also taught at Purdue University. Zorn's professional interests include complex analysis, mathematical exposition, textbook writing, and the role of mathematics among the liberal arts. He is also interested in using computer graphics and computer algebra systems to help students learn, explore, and "own" mathematical ideas. Zorn has served on many MAA committees and programs over the years. From 1996 to 2000, he was Editor of MAA's expository journal Mathematics Magazine. His latest textbook, Understanding Real Analysis, was published by AK Peters in 2010
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