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Good Math by Mark C. Chu-Carroll

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16Cantor’s Diagonalization: Infinity Isn’t Just Infinity

Set theory is unavoidable in the world of modern mathematics. Math is taught using sets as the most primitive building block. Starting in kindergarten, children are introduced to mathematical ideas using sets! Since we’ve always seen it presented that way, it’s natural that we think about set theory in terms of foundations. But in fact, when set theory was created, that wasn’t its purpose at all. Set theory was created as a tool for exploring the concept of infinity.

Set theory was invented in the nineteenth century by a brilliant German mathematician named Georg Cantor (1845--1918). Cantor was interested in exploring the concept of infinity and, in particular, trying to understand how ...

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