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When Numbers Grow Up: Sets, Partitions, and Symmetry -
At a glance, taking products of finite sets is a lot like multiplication, and unions look a lot like addition. But there’s more data in this world of set arithmetic than there is in the integers. When our sets come equipped with symmetries, thinking about exponentiation naturally leads us to representation theory, algebraic topology, and some open questions that you (yes, you!) can contribute to. 

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