Des théorèmes mathématiques prouvés en un tweet

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 maths tweet

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Tiny Proof @tinyproof

Let T:X->X be continuous on complete metric space X, d(T(x),T(y))<=αd(x,y), α<1. Then {T^n(x_0)} is Cauchy, and its limit satisfies T(x)=x.
4:32 PM - 01 avr. 13

Tiny Proof @tinyproof
By the Taylor expansion of e^z, e^(ix) = Σ(ix)^n/n! = Σ((-1)^n/(2n)!)x^(2n) + iΣ((-1)^n/(2n+1)!)x^(2n+1) = cos(x) + i*sin(x).
4:16 PM - 01 avr. 13

 

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