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May
8
comment Looking for Open Source Math Software with Poor Documentation
I upvoted for your charity intentions solely. Felt right.
May
7
comment Existence of a holomorphic function with the desired property
@learnmore Linear maps are holomorphic, what are the linear maps $ℂ → ℂ$? Which one of these restrict to $D → D$?
May
7
comment Existence of a holomorphic function with the desired property
@Blake $f(D) ⊂ (\overline D)° = D$.
May
7
answered Existence of a holomorphic function with the desired property
May
7
comment Existence of a holomorphic function with the desired property
$\frac{3}{4}·\frac{1}{3} = \frac{1}{4}$ and $\lvert\frac{3}{4}\rvert < 1$. Otherwise, use the open mapping theorem and the Schwarz lemma.
May
7
revised Connected spaces where all subsets are either open or closed
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May
7
comment Connected spaces where all subsets are either open or closed
@bof Ah, neat. Thanks. One-point spaces being the least interesting examples imaginable, though. But the link actually proves there are no other.
May
7
revised Connected spaces where all subsets are either open or closed
added 155 characters in body
May
7
revised Connected spaces where all subsets are either open or closed
edited body
May
7
asked Connected spaces where all subsets are either open or closed
May
6
comment A path to more advanced math topics.
I already upvoted it, but I’d like to verbally support the recommendation made by Hasan as well: If you know about matrices, determinants, vectors, vector products and such and you are intrigued by algebra, chances are you will find linear algebra extremely enlightening. It’s probably the most natural thing to go to if you want to get introduced to more abstract and structural mathematics. It is also helpful, if not necessary, for studying multivariate calculus and abstract analysis – which would be the next step on the calculus path.
May
6
comment Definition of a prime
“Now, $6$ is not a unit in $ℤ$” is what that should read.
May
6
comment formal power series expansion for square root
@OneWingedPterodactyl And the index in the sum is $n$, not $i$.
May
6
comment formal power series expansion for square root
Hm, your series suffers from index sickness.
May
6
revised Why does an isomorphism need to be a homomorphism?
added 2 characters in body
May
6
answered Why does an isomorphism need to be a homomorphism?
May
6
comment Why does an isomorphism need to be a homomorphism?
Also, I think this answer is missing the point of the question.
May
6
comment Why does an isomorphism need to be a homomorphism?
By saying “which admits a two-sided inverse” and leaving out the part where it’s mentioned that this inverse should be a homomorphism as well, you’re hiding the whole point you are making.
Apr
30
comment If $H$ is a cyclic group of even order, $H$ has exactly two elements which square to $1.$
There are finite abelian groups that only do have one element of order $2$, yet are not cyclic. Take $ℤ/2ℤ × (ℤ/3ℤ)^2$.
Apr
30
revised If $H$ is a cyclic group of even order, $H$ has exactly two elements which square to $1.$
added 398 characters in body