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Jan
5
revised Why the generating function of $\frac{2^K}{k!}$ is $e^{2x}$ instead of $e^{2^{x}}$?
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Jan
5
comment Why the generating function of $\frac{2^K}{k!}$ is $e^{2x}$ instead of $e^{2^{x}}$?
Yes. But my problem is that using $y=2x$ is just like a lucky guess. It could be anything, is there any systematic method that shows precisely that $y$ must be $2x$?
Jan
5
asked Why the generating function of $\frac{2^K}{k!}$ is $e^{2x}$ instead of $e^{2^{x}}$?
Jan
4
comment A challenging calculus question about differentiation
A small hint: There are weird voting philosophies on MSE.
Jan
4
comment A challenging calculus question about differentiation
This implies that you also need to ask the upvoters why they upvoted it too.
Jan
3
comment Would it be possible to extract all the points in the area and still have positive area?
General rule from what? I know that historically, finitism made more sense and infinite processes were developed more of less when set theory was developed.
Jan
3
comment Would it be possible to extract all the points in the area and still have positive area?
You're telling me that I can't. But you're not telling me why, which is the important point. Given that axiom system, there's nothing that forbids me of doing that. There is no axiom that says: It's not possible to have infinite uses of $(3)$ or something similar. The problem with your argument is that, you're assuming things based on hand waving. "It's not possible because it does not work that way, it's not possible because Jesus told me that in a dream." and so on.
Jan
3
comment Would it be possible to extract all the points in the area and still have positive area?
The problem is that you made up the part of "there is no way", you're coming with that from somewhere else. The axioms I used do not imply that I can't. That's my problem, I also can invent premises from somewhere else that enable me to make sense of it.
Jan
3
comment Would it be possible to extract all the points in the area and still have positive area?
But in the axioms, nothing forbids me of having an infinite removal, no? Perhaps in the axioms of measure theory (which I'm still too stupid to understand).
Jan
3
accepted Is there only one continuous-everywhere non-differentiable funtion?
Jan
3
asked Would it be possible to extract all the points in the area and still have positive area?
Jan
3
comment Proving that a set is measurable and has a zero area
@EamesCobb You needed to tell what definitions you were using. Is this an exercise from Apostol's book? I made the following: math.stackexchange.com/questions/1089493/…
Jan
3
asked Proving that a point is measurable and has zero area.
Jan
3
comment What's umbral calculus about?
Thanks. I have one stupid question, why is checking the OEIS important? Is it because if one process in - say - combinatorics generates one sequence and another process in - say - analysis generates the same sequence, there is a connection between them? Can you provide-me a not too hard example in which that connection is important? (presuming my suggestion is the real reason why the OEIS checking is important).
Jan
2
comment What's umbral calculus about?
Could you recommend some really elementary introduction to umbral calculus? It seems really interesting, but I still don't have much background.
Jan
2
comment What's umbral calculus about?
I'm having introductory lectures in combinatorics. I'm amazed that Umbral Calculus is a lot similar to some of the things I've seen there, I thought it was nearer to real analysis. Although, as you pointed in the start of the text: It might have a lot of connections.
Jan
2
accepted What's umbral calculus about?
Jan
2
comment Is there only one continuous-everywhere non-differentiable funtion?
@Rahul Yes, I assume I'm arbitrarily stupid too. But I've already made some questions in which it was clear that the answerer read only the question, not the text. And it was precisely what user1537366 assumed here.
Jan
2
comment Is there only one continuous-everywhere non-differentiable funtion?
@user1537366 Yes, it's normal. The economic system of MSE is driving users to comment/answer without careful reading/thought. People reply to what they see in the question but they don't read the text. In the anxious movement to get more reputation points they shoot something almost instinctively.
Jan
2
comment Is there only one continuous-everywhere non-differentiable funtion?
@regret Yes. But mathematics is like a set of doors, if you open one, there are infinite other doors. And then if you choose one of these new doors, sometimes you find a connection between two doors, sometimes you open more and more doors. Who knows what those guys at Princeton's Institute for Advanced Study are thinking by now?