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22h
revised Are there infinitely many $N^3$ (especially for prime $N$) that cannot be expressed as a sum of three positive cubes?"
some formatting (more may be needed)
23h
suggested approved edit on Are there infinitely many $N^3$ (especially for prime $N$) that cannot be expressed as a sum of three positive cubes?"
23h
comment How to solve current exponential equation?
The power $a^x$ is well-defined also if $a$ is real and positive and $x$ is a complex number, so I wonder what the complex solutions $\{ x\in\mathbb{C} \mid 3^x + 7^x = 21^x \}$ looks like.
Jan
23
comment Can a complex number ever be considered 'bigger' or 'smaller' than a real number, or vice versa?
Also note that this is not a total order unless you choose some (arbitrary?) convention on how to compare numbers like $5+2i$ and $2-5i$ (for example) whose distances from zero are identical.
Jan
23
comment Soft question: Union of infinitely many closed sets
You: I can imagine that if there are nested disks inside each other, that in this case the union would clearly be closed. No, not with an infinite number of disks. For example let $A_n$ be the closed disk in the $x$-$y$ plane with radius $( 7-\frac1n )$. Then the union $\bigcup_{n \in\mathbb{N}} A_n$ is not closed. Actually it is an open disk.
Jan
23
comment Is there a maximum value between open (0,1) set?
@coffeemath As soon as we define enough to make $1/10^\infty$ meaningful, that quantity will be the real number $0$, so it is real. Only some "sub-expressions" within it are not real. The problem is that the supremum of the interval, which is $1$ or (fancily) $1-\frac{1}{10^\infty}$, is not a member of that interval.
Jan
21
comment examples of functions with vertical asymptotes in real life
According to the Big Rip hypothesis for the expansion of the universe, the "scale factor" (or the distance between two given non-related galaxy clusters) will tend to infinity as the age of the universe tends to some finite value (image).
Jan
21
comment examples of functions with vertical asymptotes in real life
Wikipedia has an article hyperbolic growth. Something that grows like that will become infinite in finite time (vertical asymptote). Maybe the Applications section can inspire you? If you find better examples, you could add them to the Applications section there.
Jan
19
comment Is a point a neighbourhood?
A more general definition of neighborhood often used says $N$ is a neighborhood of a point $x_0$ iff $x_0 \in U \subseteq N$ for some open set $U$. Otherwise, your answer is correct, of course.
Jan
19
comment Can a neighbourhood of a point be an singleton set?
For that sake $X$ could be the natural numbers with the standard metric, $d(x, y) = |y-x|$.
Jan
19
comment Can you be 1/12th Cherokee?
@AsafKaragila chucknorrisfacts.com got that one wrong.
Jan
18
comment What's your favorite proof accessible to a general audience?
How do you assign a "generation" to an individual? How is "incest" defined here? Is having offspring with one's seventh cousin twice removed "incest" here? Since that term is non-constant among cultures it needs a definition.
Jan
16
comment Prove that a statement or its negation follows from ZFC
Here is another statement that can be decided in principle: All Fermat numbers $2^{2^n}+1$ with $5 \le n < 50$ are composite.
Jan
5
comment Sine of a Complex Number
It is well-known that solving $\sin x = a$ when $-1<a<1$ leads to two sequences of solutions, $x = x_1 + 2k\pi, k\in\mathbb{Z}$ and $x = x_2 + 2k\pi, k\in\mathbb{Z}$. Your answer suggests that the same happens more generally, only with non-real $x_1$ and $x_2$. It is easy to see that sine as a function of a complex variable has period $2\pi$ just like the real sine function.
Jan
4
comment How can we measure how “irrational” a number is?
You say on the irrationality measure of $\pi$ that we might suspect that it greater than 2. However we could also conjecture that it is 2. Almost all numbers (with respect to Lebesgue measure) have irrationality measure 2, so why would $\pi$ be unusual? The only thing that is known, is that the irrationality measure of $\pi$ is in $\left[ 2, 7.60630853 \right)$.
Dec
30
comment Are set differences in a sigma algebra?
Or maybe as $(A^c \cup B)^c$.
Dec
29
comment What parts of a pure mathematics undergraduate curriculum have been discovered since 1964?
Wikipedia refers Carleson's 1966 paper which would make this within the 50 years period. Carleson is still alive.
Dec
27
comment curvature proof
Do you use the formula $\kappa = \frac{f''}{\left( 1+(f')^2 \right) ^{3/2}}$?
Dec
25
comment Powers containing every digit equally often
See more at Sloane's A074205.
Dec
22
comment Rank of a general matrix
The matrix $M=AB$ for particular matrices $A,B$. Do you know anything about the rank of a product?