Smaller Is Better: Why Finite Number Systems Pack More Punch


Making Sugar
Feb 24, 2016
It’s one thing to turn a cartwheel in an open field. It’s another to manage it in a tight space like a bathtub. And that, in a way, is the spirit of one of the most important results in number theory over the past two decades.

The result has to do with the “sum-product problem,” which I wrote about last week. It asks you to take any set of numbers and arrange them in a square grid, then fill in the grid with either the sums or the products of the crosswise pairs.

The sum-product problem states that the number of distinct sums or products will always be close to N2 (where N stands for the number of numbers used to make your grid).
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