VCU Mathematics Department Colloquium

 

Friday November 13th, 2009 at 3:00

Location: Temple Building Room 1165

Professor Joel Hamkins, College of Staten Island, CUNY

Joel Hamkins received his B.S. in mathematics from Caltech in 1988, and Ph.D. in mathematics at UC Berkeley in 1994, under W. Hugh Woodin. He is currently a full Professor at the Mathematics Program at the CUNY Graduate Center and an organizing member of the CUNY Logic Workshop. He has previously held positions at Kobe University, Carnegie Mellon University, Georgia State University and the Universität Münster. Professor Hamkins’ personal webpage is found here. http://nylogic.org/Workshophttp://nylogic.org/Workshophttp://jdh.hamkins.org/shapeimage_2_link_0shapeimage_2_link_1shapeimage_2_link_2

Fun and paradox with large numbers, logic and infinity


What is the largest natural number that can be written or described on a 3x5 index card?  Which is bigger, a googol-bang-plex or a googol-plex-bang? Are there some real numbers that cannot be described?  How many continuous functions are there on the reals?  Is every natural number interesting?  Is every sentence either true or false or neither true nor false?  Can one ever complete a task involving infinitely many steps?  We will explore these and many other puzzles and paradoxes involving large numbers, logic and infinity, and along the way, learn some interesting mathematics.