"Binary Numbers and Different Sizes of Infinity"
featuring Julia Bennett

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Georg Cantor's diagonalization argument is one of the deepest and most powerful ideas of 19th-century mathematics, a gateway to fundamental discoveries in set theory and computer science. It was first used to prove that infinities come in various sizes, at a time when most mathematicians didn't even believe infinities could be treated as legitimate mathematical objects.

Binary numbers are a simple and ancient number system, a workaday tool in arithmetic and computer engineering. How high you can count is limited only by how many binary digits you can keep track of.

On October 12, 2014, graduate student Julia Bennett showed us that by thinking about binary numbers, and how they're used to count finite collections of things, we could rediscover the diagonalization argument, which is all about counting infinite collections of things. We also caught a glimpse of some of the deep questions in set theory to which diagonalization opened the way.

Printable version of the flyer