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1d
comment How to insert Gothic letters in Word?
That’s not a math question, though.
1d
accepted Are binomial series multiplicative in their bases?
1d
asked Are binomial series multiplicative in their bases?
May
21
answered Proving that the ball is converx
May
21
comment Proving that the ball is converx
Invoke the definition of convexity and the triangle inequality.
May
15
comment If a field extension contains a cyclotomic extension is it solvable?
Recall that a solvable group requires a subnormal series in which all factors are abelian. What can you really say about $\mathrm{Gal}(L/M)$? As an extreme case, take any non-solvable extension $L/K$ and choose $M = K$, which trivially is a cyclotomic extension.
May
9
comment How to teach Mathematical Induction mathematically?
Unfortunately, in order to make it possible for others to help, you would have to list everything that you have tried so far, forcing you to relive your painful experience.
May
9
comment Some very short clarification on quotient groups
@elDin0 No. Your problem is on set-theoretic level: It seems like you are not differentiating between an element of a set and an element of an element of a set. Take your favorite mathematical starting object $x$ (if you’re a minimalist, choose $x = ∅$, the empty set) and then consider $y = \{x\}$ and $z = \{y\}$. Then $z ≠ \{x\}$ because the only element of $z$ is $y = \{x\}$ and $x ≠ \{x\}$. Likewise, $\{A_3, (1~2)A_3\} ≠ \{ \text{elements of $A_3$}, \text{elements of $(1~2)A_3$}\}$.
May
9
comment Some very short clarification on quotient groups
Do you know the isomorphism theorem for groups? How is $A_3$ defined for you? Do you know how many elements $A_3$ and$S_3$ have?
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
added 44 characters in body
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.