OEIS A00007: Characteristic function of the set {0}

A deceptively simple sequence—1, 0, 0, 0...—serves as the indicator for the singleton set {0}. We explore why this tiny sequence pops up in unexpected corners of mathematics: the alternating sums of rows in Pascal’s triangle, its role as the identity element under Dirichlet multiplication, and even its connection to the zero-to-the-zero power debate. Through these connections, we glimpse how a humble sequence can illuminate deep structure in number theory and the philosophy of math.

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