Buckets, balls, and the Axiom of Choice

02/20/2014 - 4:30pm
02/20/2014 - 5:30pm
Jay Williams (California Institute of Technology)

Suppose you had infinitely many balls in infinitely many buckets. A mathematical principle called the Axiom of Choice says that there is a way to pick one ball from each bucket. But if we don't let ourselves use this axiom, then we'll find ourselves perplexed; there will be some buckets from which we can't pick any ball. Even though every bucket contains a ball, to us it looks like there are more buckets than balls! Come to this talk to find out how this strange turn of events comes to be.

About the Speaker:

Jay Williams is a postdoctoral scholar and Harry Bateman Instructor at the California Institute of Technology. He received his Ph.D. in Mathematics from Rutgers University. While there, he received the Rutgers School of Arts and Sciences Graduate Excellence Fellowship. His research focuses on connections between group theory and logic. Much of his work is on the complexity of various group-theoretic classification problems, for which he recently obtained some important results.

Kravis Center LC62 (Freeburg Forum), Claremont McKenna College
Misc. Information: 

Refreshments served at 4:15 p.m. See attachment for the flyer.

CalTech_logic.pdf110.86 KB

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