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I'm a student of mathematics in Germany.


Jan
20
revised What is the difference between coordinates transformation and change of coordinates?
added 9 characters in body; edited tags
Jan
20
comment Question about cyclic subgroup of a non-abelian group of order $8$.
@Libertron Yes, of course I did.
Jan
20
revised Question about cyclic subgroup of a non-abelian group of order $8$.
deleted 3 characters in body
Jan
19
answered Question about cyclic subgroup of a non-abelian group of order $8$.
Jan
18
comment is complex number under absolute value a group?
@jeniffer Not sure, why it’s that long: For $a, b, c ∈ ℂ$: $$\begin{align*} (a*b)*c &= |ab|*c = ||ab|·c| = |ab|·|c|\\ &= |abc|\\ &= |a|·|bc| = |a·|bc|| = a*|bc| = a*(b*c) \end{align*}$$
Jan
18
comment is complex number under absolute value a group?
@jeniffer Yes, that’s what I mean. The notion of an inverse (for $a ∈ ℂ$ some element $a' ∈ ℂ$ such that $a*a' = e$ and $a'*a = e$, the identity) doesn’t make any sense if there isn’t an identity to begin with. Also note, that with the same argument the operation doesn’t even yield a group (/monoid) when restricted to $ℝ$.
Jan
18
revised is complex number under absolute value a group?
added 17 characters in body
Jan
18
comment is complex number under absolute value a group?
No, $1$ is no neutral element. Maybe I did misunderstand your answer, though?
Jan
18
answered is complex number under absolute value a group?
Jan
18
comment Extension Fields, complex numbers.
On understanding the argument: Have you heard of the omni-important isomorphism theorem (for rings) yet? If not, look at it. As soon as you got that, take as a first example the ring homomorphism $ℝ[X] → ℂ,~X ↦ \mathrm i$ and determine its kernel.
Jan
18
comment Canonical forms, Linear algebra
Your efforts etcetc?
Jan
18
comment $A\subset f^{-1}(f(A))$ with equality if and only $f$ is injective.
@idm What do you consider your proof? And of which statement exactly?
Jan
18
answered $A\subset f^{-1}(f(A))$ with equality if and only $f$ is injective.
Jan
18
comment Introducing $\mathrm π$ and polar coordinates in real analysis
Thanks! For this approach, Taylor’s theorem is used.
Jan
18
comment Introducing $\mathrm π$ and polar coordinates in real analysis
@ChristianBlatter Thanks! These are nice lecture notes! From skimming over them, the proofs are a bit too geometrical/rely a bit too much on geometric intuition for my taste. I like them nonetheless.
Jan
18
revised Introducing $\mathrm π$ and polar coordinates in real analysis
grammar
Jan
18
revised Introducing $\mathrm π$ and polar coordinates in real analysis
grammar
Jan
18
asked Introducing $\mathrm π$ and polar coordinates in real analysis
Jan
18
comment Existence of continuous angle function $\theta:S^1\to\mathbb{R}$
By the way, it should read “for all $z ∈ U$”.
Jan
18
comment Existence of continuous angle function $\theta:S^1\to\mathbb{R}$
How did you prove the injectivity of $θ$? Furthermore, how did you conclude that $θ\colon S^1 → θ(S^1)$ is not only a bijective continuous map, but a homeomorphism?