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I'm a student of mathematics in Germany.


Nov
24
comment Show that it is/is not a normal extension
What’s a canonical extension? Oh, you probably mean a normal extension!
Nov
24
answered Closedness and boundedness in metrizable topological spaces
Nov
24
answered Periodic functions and limit at infinity
Nov
24
answered Creating surjective holomorphic map from unit disc to $\mathbb{C}$?
Nov
24
comment Extension theorem for locally Lipschitz functions
Isn’t $(0..∞) → ℝ,~x ↦ 1/x$ locally Lipschitz?
Nov
24
comment How prove this $n$ smaller cubes ( length is $1,2,3,\cdots,n$) can't Mosaic a big cube
@Henry: This is probably implied by “length is $1, 2, 3, …, n$.”
Nov
22
comment Solving $(1-x)^3 = -1$ over the complex field
Do you want a solution in the form of $a + ib$? Can you guess the solutions for $z^3 = -1$ by geometric interpretation?
Nov
21
answered Find remainder when $2^{30}\cdot 3^{20}$ is divided by $7$ without using calculator
Nov
18
comment Why is $0^0$ also known as indeterminate?
You will need to explain the bar notation a bit more. Is $1||4^0 = 1·4^0$?
Nov
18
comment Fundamental group of sphere
@Sasha $π_1(S^2) = \text{trivial group}$ and $\text{trivial group} × ℤ = ℤ$. You can write the trivial group as $0$ or $1$ (depending on whether you want to write your group operations multiplicatively or additively).
Nov
18
comment Fundamental group of sphere
@Sasha Write it as $1 × ℤ = ℤ$. (I’m assuming you were confusing $0$ as the trivial group with the empty set $∅$ and thought $0 × ℤ = 0$.)
Nov
17
comment $f_n$ converges uniformly on compact subsets of $\Bbb D$ to the unique conformal map $f: \Bbb D \to D$ s.t $f(0)=z_0$, $f'(0)>0$
Context, former attempts, etc.?
Nov
16
comment is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
Do not assume that they are in $ℤ/7ℤ$! Assume you have a a degree two factor $g ∈ ℤ/7ℤ[X]$ of $f$. Assume there is a ring $R$ such that $ℤ/7ℤ \subseteq R$ with elements $α, β ∈ R$ such that $g$ splits as $g = (X - α)(X - β)$. It’s okay to assume that, because $R = ℤ/7ℤ[X]/(g)$ with the natural inclusion of $ℤ/7ℤ$ has the above mentioned properties, so you can work there. You can’t say $α ∈ ℤ/7ℤ$ or $β ∈ ℤ/7ℤ$ a priori, but you can say that $α^5 - 1 = 0$ and $β^5 - 1$, because they both are roots of $g$, and therefore roots of $f$ and therefore roots of $X^5 - 1$.
Nov
16
revised is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
included note/warning
Nov
15
comment is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
@Lubin. Hm, why?
Nov
15
revised is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
added 26 characters in body
Nov
15
answered is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
Nov
15
comment Instructive sources for arguing without elements
@MartinBrandenburg You plan to write one? That’s great news! But how about graduate level books?
Nov
13
asked Instructive sources for arguing without elements
Nov
13
answered Show that there is an $R$-module homomorphism $\bar{h}$ such that $g \circ \bar{h} = h$.