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Where is the assumption $0\in B$ used in Nathanson's generalization of Cauchy-Davenport (Theorem 2.1)?

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Note that $$\frac {1} {1+x}=\sum_ {n \ge 0} (-1)^nx^n$$ Integrating both sides gives you \begin {align} \ln (1+x) &=\sum_ {n \ge 0}\frac { (-1)^nx^ {n+1}} {n+1}\\ &=x ...

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Binomial expansion of $ (1-x)^n$ Ask Question Asked 11 years, 6 months ago Modified 5 years, 1 month ago Viewed 250k times

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Well, calling Ln (-1) = i*Pi is already expanding the standard definition of Ln. In the context described (where A & -A are both real, and the log used is standard), Ln (-1) is undefined. But I'd say the …

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I know the definitions of the $1$ and $2$ norm, and, numerically the inequality seems obvious, although I don't know where to start rigorously. Thank you.