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Actually it is Calculus in p-adic numbers!
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Mmmmhhhh, sure? Because p-adic numbers have characteristic 0, AFAIK.
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The technical term is "formal derivative" b/c there are no limits involved, it's basically a rewrite rule for changing x^n to nx^(n-1).
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I know, yes, but did not want to digress. Thanks though. Actually, it is the "extension" to K[e] with e^2=0, as "usual".
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The infinitesimally thickened point.
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