Ben Crowell
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 2d awarded Nice Answer Mar31 awarded Good Question Dec15 awarded Popular Question Sep24 awarded Autobiographer Aug18 awarded Popular Question Aug4 comment In calculus, which questions can the naive ask that the learned cannot answer? +1, but I don't think a naive first-year calc student would be at all likely to come up with this series. It takes a lot of insight to understand why its convergence is difficult to establish, and why the exponents 3 and 2 work. Aug3 revised Intuitive explanation of the difference between waves in odd and even dimensions Kevin Brown is the mathpages guy, not John Baez Jul26 comment Could we assign a numerical value to an infinitesimal? I don't understand the point of the question. When I first read it, I thought maybe you were trying to reinvent the wheel, and you just needed to be told about the existence of systems such as non-standard analysis (NSA) and smooth infinitesimal analysis (SIA). But then I saw in one of your comments that you had already heard about SIA. So what is this question asking? Are you proposing a third system and asking whether it's useful or consistent? Jul26 comment What are some conceptualizations that work in mathematics but are not strictly true? @EricLippert: Symbols like $dy$ and $dx$ can be defined as infinitesimal numbers. That's historically what they originally meant, and there's nothing wrong with it. See math.stackexchange.com/questions/21199/… Jul22 awarded Yearling Jul20 comment Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small? @jpmc26: The foundational aspects of calculus have gone through a series of changes over the centuries, and therefore different people have different ideas about the meaning of a symbol such as $d\Phi$. The original meaning was that it was an infinitesimal number. That fell out of favor ca. 1850-1960, when the foundations of calculus were rebuilt in terms of limits. Then infinitesimals, which scientists and engineers had never stopped using, were rehabilitated. A nice book on this topic at the undergraduate level is Keisler, math.wisc.edu/~keisler/calc.html Jul14 awarded Popular Question Jul13 comment Formalizing Those Readings of Leibniz Notation that Don't Appeal to Infinitesimals/Differentials Related: math.stackexchange.com/questions/865559/… . I think the basic issue you're running into is that Leibniz notation predates the notion of a function by a couple of hundred years. Leibniz and his contemporaries thought in terms of expressions, not functions, and the notation implements that attitude. Jul12 asked Modern notational alternatives for the indefinite integral? Jul10 comment Best applications-oriented introductory calculus textbooks? Agnew may actually be public domain now. Its copyright was in 1962, and it doesn't appear to have been renewed. Jul2 awarded Curious Jun24 revised Standard terminology for infinite limits with opposite sign on the two sides? added 265 characters in body Jun24 comment Standard terminology for infinite limits with opposite sign on the two sides? @Omnomnomnom: I should have specified: it is sometimes the case that it would be considered wrong to say that the first limit does not exist OK, if the terminology is not totally standardized then that would be good to know. However, in the small sample of books I have handy on paper or online, all seem to define the first limit as not existing. Jun23 comment Standard terminology for infinite limits with opposite sign on the two sides? @mm-aops: So how would you distinguish the two cases in the question? #1 "has an infinite limit," while #2 "has no finite or infinite limit?" Jun23 comment Standard terminology for infinite limits with opposite sign on the two sides? We talk about "lateral limits". The limit with "+" is the limit from the right, and the other is the limit from the left. Yes, I understand that. One could certainly describe them as "a limit that is infinite and has the same sign from both sides" versus "a limit that is infinite and has opposite signs from the two sides." However, that would be very cumbersome.