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Mar
10
comment Show that $f(z)$ has no antiderivative in $\,S=\mathbb{C}\setminus \{-i,i\}$
In the third solution, the repetition for $z=-i$ is not necessary - you have already proven that the antiderivative does not exist in the given area.
Mar
10
comment Show $I=\{sf\mid s\in \mathbb Z_{11}[x]\}$ matches $J=\{h \in \mathbb Z_{11}[x] \mid h(1) = h(-2) = 0\}$.
@haunted85: Those are just the roots of $f$.
Mar
10
comment Show $I=\{sf\mid s\in \mathbb Z_{11}[x]\}$ matches $J=\{h \in \mathbb Z_{11}[x] \mid h(1) = h(-2) = 0\}$.
$f(\overline 2)=\overline 4$ so $f\not\in J$ but $f\in I$ with $s=1$. So $I\neq J$
Mar
10
comment Show $I=\{sf\mid s\in \mathbb Z_{11}[x]\}$ matches $J=\{h \in \mathbb Z_{11}[x] \mid h(1) = h(-2) = 0\}$.
In the definition of $I$, don't you mean $s\in\mathbb{Z}_{11}[x]$?
Feb
9
comment What is inverse of $I+A$?
By substituting $A'=A-I$, you are basically asking for the inverse of all matrices.
Feb
6
comment Example of an increasing, integrable function $f:[0,1]\to\mathbb{R}$ which is discontinuous at all rationals?
@Belgi: that depends on your measure...
Jan
31
comment A box contains 150 oranges.If one orange is taken…
@AndréNicolas: I read it as a "factory of boxes" question, in which some process generates uniformly distributed rotten oranges. If you know the probability for this exact box, then apparently you have already counted the rotten ones.
Jan
31
comment A box contains 150 oranges.If one orange is taken…
Strictly speaking, we don't know the number of good oranges. There could be 150 bad oranges in the box. We can only give the estimated number of good oranges.
Jan
30
comment Next number after 1729??
Of course, in Haskell, you wouldn't need to stop anywhere. You can just calculate them all and print a finite subset.
Jan
21
comment Filter signal through convolution
@Kristian: Oh, then perhaps you haven't reached this yet, but convolution in the time domain is multiplication in the Fourier domain. So just take the Fourier transform of both, multiply, and detransform.
Jan
21
comment Filter signal through convolution
Why don't you use fourier analysis? You correctly tagged it as such.
Jan
20
comment Solution of integration of $e^{x^2}$
@MårtenW: I must admit I missed that, but of course this can be solved by some appropriate complex substitution.
Jan
20
comment Solution of integration of $e^{x^2}$
By "elementary", we mean "elementary functions", such as taking powers and multiplying and addition. There is no expression for the integral $e^{x^2}$. We can only give it a name (specfically the "error function"). I don't know how one can prove this.
Jan
15
comment Is $f = x^2$ or only $f(x) = x^2$ correct?
if, by $x$, the /variable/ is meant, then I do not see how that would be incorrect. You are right however, that (in words) "plugging in a value" produces a new "value".
Jan
15
comment Is $f = x^2$ or only $f(x) = x^2$ correct?
So why is your view correct? Under my view, the notation is correct (albeit confusing, since I am leaving away all the isomorphisms), but under your view, it is not.
Jan
15
comment Is $f = x^2$ or only $f(x) = x^2$ correct?
Not quite - $x$ is not some value, but instead a variable. In that case, $x^2$ can be seen as an element of $\mathbb{R}[x]$, the ring of polynomials, which is isomorphic to a subset of the ring of continuous functions.
Jan
8
comment Mathematics, Philosophy and writing.
Perhaps more famous for his literature than his mathematics: Charles Dodgson / Lewis Caroll.
Jan
5
comment Learning category theory before abstract algebra
I think categories inherently have group-like properties, so I'd suggest you learn abstract algebra first. Though strictly speaking, neither relies on the other, so you can give it a shot.
Jan
5
comment In a ring homomorphism we always have $f(1)=1$?
Could you add a word on why we want to rule out such mappings?
Jan
2
comment a problem on the topological properties of a annulus
Please fix ambiguous terminology: to say a map is open or closed usually refers to its graph having such properties.