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Mathematics
Topology and Analysis
What uniquely characterizes the germ of a smooth function?
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[QUOTE="lugita15, post: 6052021, member: 74861"] Yes, if we define a partial order on the set of all functions infinitely differentiable at 0 by saying that f<g if the limit of f(x)/g(x) as x goes to 0 = 0, and then take a maximal totally ordered subset of that partially ordered set, then the order type of that set will be much bigger than the order type of the real numbers. It will basically be order-isomorphic to the set of all surreal numbers with birthday less than omega_1 (the first uncountable ordinal). See [URL='https://math.stackexchange.com/a/2878059/71829).']here.[/URL] [/QUOTE]
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What uniquely characterizes the germ of a smooth function?
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