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Feb
7
comment Zero to the zero power - is $0^0=1$?
To say something is undefined you should be sure nobody defined it.
Dec
19
comment Zero divided by zero must be equal to zero
You can define division this way, but it is not the only possible way, actually. One can define 0/0=0 and have everything fine in a ring (not only empty ring).
Dec
18
comment Zero divided by zero must be equal to zero
The second statement does not follow from axioms of ring. Division is not defined on rings.
Dec
15
comment Is there a function whose antiderivative can be found but whose derivative cannot?
@ASKASK Where in the question he says he asks for an elementary function? He asks for an integrable function whose derivative is not elementary. There is a lot of such functions.
Dec
15
comment Is there a function whose antiderivative can be found but whose derivative cannot?
totally wrong answer.
Dec
10
comment Zero divided by zero must be equal to zero
@Akiva Weinberger while such algebras can be constructed, they definitely are not natural. From the algebraic point of view it is much more natural to postulate $0x=0$ for any $x$, including $x=0$ and $x=\infty$. Similarly to how everything to the $0$ power is $1$, including $0$ and infinity.
Dec
7
comment Zero divided by zero must be equal to zero
There is no proof above that 0/0 cannot equal to 0. Or more precisely, there is a proof but it is wrong, which has been indicated.
Dec
5
comment Zero divided by zero must be equal to zero
There is an error here: $$1 = 0 + 1 = \frac{0}{0} + \frac{1}{1} = \frac{0 \cdot 1}{0 \cdot 1} + \frac{1 \cdot 0}{1 \cdot 0} = \frac{0 \cdot 1 + 1 \cdot 0}{0 \cdot 1} = \frac{0 + 0}{0} = \frac{0}{0} = 0$$. The error is in that you cannot multiply a numerator and denomenator both by zero. E.g., $\frac1{1}\ne\frac{1\cdot0}{1\cdot0}$.
Nov
28
comment The trigonometric solution to the solvable DeMoivre quintic?
You claim that a general quintic can be solved in terms of trigonometric/hyperbolic functions. But your further explanation includes theta function and eliptic integrals.
Nov
25
comment Does infinity and zero really exist?
In what theory? About what theory you are asking? If you are asking about physical world, you should ask in physics.se
Nov
21
comment Is there a name for the class of functions which are infinitely integrable in elementary functions?
There are rational functions (fractional) whose integrals are elementary.
Nov
21
comment What makes elementary functions elementary?
Real part, imaginary part, absolute value and argument are not elementary functions, it is a convention. Also your trick works only for real arguments.
Nov
7
comment Why can $2^3$ be defined but $0^0$ cannot
$0^0$ can be defined and has been by many people.
Nov
7
comment Is $\frac00=\infty$? And what is $\frac10$? Are they same? Does it hold true for any constant $a$ in $\frac{a}0$
Obviously a wrong question linked as duplicate.
Nov
7
comment Is term “real number” equivalent to “group of algorithms generating stream of digits”?
@Asaf Karagila maybe somebody would like to improve it to make it better.
Nov
7
comment a Function with several periods
@Aniket it has no smallest period but has other periods.
Nov
7
comment a Function with several periods
OK, discrete, and what?
Oct
25
comment Where in the theory of higher dimensions do Bernoulli numbers arise?
Does not it seem not to be about metric spaces?
Oct
16
comment Is Aleph 0 a natural number?
@Will R I would say number is a common property of sets of various objects whose elements can be put in bijectional relations. Of course this would not work for non-integer numbers though
Sep
10
comment How to sum up this series? $\sum_{n=1}^\infty\frac{(-1)^{n-1} B_n}{n}$
This is the reason why I needed this series, by the way: mathoverflow.net/questions/216252/…