anyone mathy here able to explain why people say it's wrong to think of df(x)/dx as a literal ratio of infinitesimal quantities?
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@CoronaCoreanici @starkatt So now that I have the time to come back to this--what makes the archimedean property fundamental? It doesn't sound like some underpinning of mathematics, it sounds more like an interesting property.
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@CoronaCoreanici @starkatt we have a vague idea of what a dedekind cut is; it's considering a number as an ordered pair of ({the set of all numbers less than it}, {the set of all numbers greater than it}), right?
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@CoronaCoreanici @starkatt it feels kind of Weird that you can do that and get ℵ₁ reals, when you only have ℵ₀ rationals. It feels like there could only be ℵ₀ ways to divide them up in a consistent manner
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@CoronaCoreanici @starkatt I thought the cardinality of the reals was ℵ₁? huh
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