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I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


Mar
11
revised Absolute convergence for all values except the values $z=\left( 1+\frac {a} {m}\right) e^{\frac {2k\pi i} {m}}$
make title not take up too much space on main page
Mar
11
comment Absolute convergence for all values except the values $z=\left( 1+\frac {a} {m}\right) e^{\frac {2k\pi i} {m}}$
Your formulas are distractingly huge. Instead of abusing \dfrac in exponents, I'd recommend using \exp(...) instead. Especially for that last formula with everything inside an e^{...}.
Mar
10
comment Tough Geometry Problem--Regular Polygon inside Circle
Complex numbers are really the natural setting for the solution to this problem. Without them, you'll need to deploy a lot of trigonometric identities. It's surely possible, but I think it won't be pretty.
Mar
10
revised Tough Geometry Problem--Regular Polygon inside Circle
added 38 characters in body
Mar
10
awarded  Announcer
Mar
9
comment Blending values on the number line
No pictures necessary, I get what you mean. It sounds like you might also want control over how heavily you smooth the transition as well, yes? It's an interesting problem; I'll think about it and post an answer if I come up with something good.
Mar
9
comment Blending values on the number line
At first glance, this looks like it could be solved by a variant of monotone cubic interpolation, but I'd still like to hear your answer to my previous comment first.
Mar
9
comment Blending values on the number line
Could you give some context on what problem you are trying to solve through this? I ask because it is a little unusual to do this sort of blending between divisions, and if we know more about what you are really trying to achieve, there may be a more natural solution for it.
Mar
9
comment Do you prove all theorems whilst studying?
Crossposted to Reddit: reddit.com/r/math/comments/qoocl . The broken link to the MathOverflow question is here.
Mar
9
comment What makes elementary functions elementary?
Throw out function inversion in general; include just the logarithm (which brings in the inverse trigonometric functions and $n$th roots).
Mar
9
comment Understanding surface area of a revolution/length of curve
Since you say you have the same question about the arc length formula, have you looked at this previous question? Intuition behind arc length formula
Mar
9
comment What makes elementary functions elementary?
I don't think you can include function inversion in your list. For one, the inverse of $x \mapsto xe^x$ is not usually considered elementary. For another, @Zsbán's comment might be referring to the inverse of $x \mapsto b = \sin x - ax$.
Mar
9
comment Definition of a point and object
This is sort of like asking about the definition of "element" in set theory, or "vector" in linear algebra. What we really care about are the collections of things (sets / vector spaces / categories) and the structure of these collections. Whatever things happen to be in the collections, we call them elements / vectors / objects. But they're not really important in their own right.
Mar
9
comment Intuition behind growth rate of some functions
Also, it's pointing out that $x^{1/x}$ is maximized at $x = e \approx 2.718\ldots$, which suggests (but doesn't prove) that the value at $x = 3$ should be greater than the other options.
Mar
9
comment Intuition behind growth rate of some functions
"[$10000^{10000/n}$] will grow at a smaller and smaller rate." Or even, not grow at all: it is a decreasing function!
Mar
9
comment What makes elementary functions elementary?
I think you have described all analytic functions, which is a strictly larger set. The error function, for example, is not elementary but its Taylor series converges everywhere.
Mar
8
comment What special function is this?
Wouldn't it be easier to just say $a > 4$?
Mar
6
comment proving that four axis-parallel rectangles whose intersection graph is a cycle delimit another rectangle
I think your approach can be distilled into the following. If $B$ does not intersect $D$, then there is some interval of $x$- or $y$-coordinates that lies strictly between them. Similarly for $A$ and $C$, and it has to be the other axis because otherwise $A$ and $C$ could not intersect both $B$ and $D$. The product of the intervals therefore intersects none of the rectangles. That seems elegant enough to me.
Mar
6
comment Relationship between $|a \cdot b|$ and $|a|$ , $|b|$
My jokes have really been falling flat today. I should stop.
Mar
6
comment Is it possible to get 1/3 without dividing by 3?
You should really draw those figures to scale; it looks like you've proved that your sum is $2/3$... By the way, a nice geometric proof that $1/4 + 1/16 + 1/64 + \cdots = 1/3$ (which is equivalent to what you're proving) is the second figure on this page.