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Higher Order Derivative Test and Germs
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[QUOTE="lugita15, post: 6044872, member: 74861"] I meant positive integers, but yeah it doesn't alter your post much. First of all, the set of all continuous functions, let alone the set of smooth functions, has the same cardinality as the set of real numbers, because a continuous function is defined by its values on the rational numbers. Second of all, I'm not saying I want an injection. Just like the function which maps the set of all smooth functions to their second derivative at ##0## isn't an injection, but still if you take two random functions the chance that they'll have the same second derivative at ##0## is very small, I want a function ##F## such that if ##y_1\neq y_2##, then the chance that ##F(y_1) = F(y_2)## is very small. [/QUOTE]
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