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2d
comment How to insert Gothic letters in Word?
That’s not a math question, though.
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
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
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
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
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
comment If $ f : S^n \to R^n $ satisfies $f(-x)=-f(x)$ for all $x \in S^n $,then there exists $ y \in S^n $ with $f(y)=0 $
@SaikatBasu If $f$ isn’t assumed to be continuous, then the statement is obviously false. Just partition $S^n$ into antipodal sets $S^n = T \sqcup -T$ and take any function $f \colon T → ℝ^n$ with no zeros. Then extend it to $S^n$ such that $f(-x) = -f(x)$ $∀x ∈ T$.
Apr
28
comment Can all “standard” properties of the tensor product be proven from the universal property?
For example, if $ψ\colon V × W → V \otimes W$ is the bilinear map from the universal property, and $V$ and $W$ are free with bases $B ⊂ V$ and $C ⊂ W$, then for all vector spaces/moudles $Z$ and all maps $ψ(B × C) → Z$, there is a map $B × C → ψ(B×C) → Z$ and so there is exactly one bilinear map $V × W → Z$ extending this map and so there is, by the universal property of tensor products, exactly one linear map $V \otimes W → Z$ commuting with $ψ$ and the extended bilinear map on $V × W$, so extending the map $ψ(B × C) → Z$ - therefore, $ψ(B × C)$ is a basis of $V \otimes W$.