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6m
comment Is the sphere with points deleted a topological group?
This paper is of interest with regards to part (d): raczar.es/webracz/… PDF warning. You can identify the two points removed with $\Bbb C^*$ (by sending one point to infinity and the other to zero) which is a topological group.
24m
comment Which irrational number represents the infinite simple continued fraction [0;7]?
Write it as $x = \frac{1}{7+x}$ instead.
1h
comment Why is the Fundamental Theorem of Arithmetic so important?
It serves as the basis for a lot of number theory and algebra, in some sense.
21h
comment In a finite dimensional inner product space with $T ∈ L(V)$, show that $\langle u,v\rangle = \langle T(u),T(v)\rangle$ implies $T$ is invertible.
This looks good to me!
21h
comment multiplication of finite sum (inner product space)
Question: maybe I am off base here, but is it actually well-defined notation to have two sums with the same index?
21h
comment multiplication of finite sum (inner product space)
You should have an extra factor of $3$ at the end, however I am not totally conviced that having two sums with the same index is actually well-defined.
21h
comment Is that true that not every function $f(x,y)$ can be writen as $h(x) g(y)$?
@Rodriguez Try plugging in $y=1$ or $x=1$.
23h
comment Example of a diffeomorphism from all of $\mathbb{R}$ to itself
I'm guessing you want a non-trivial one?
1d
comment What is the name of that theorem?
This reminds me of the Sampling Theorem in some sense.
1d
comment For a normal operator is it true that $\|T^*T^2\| = \|T^3\|$?
I tried to keep it as general as possible for that reason, particularly because of the use of the word "operator." That's almost never used in regular linear algebra parlance.
1d
answered For a normal operator is it true that $\|T^*T^2\| = \|T^3\|$?
1d
comment A fierce differential-delay equation: df/dx = f(f(x))
What is $b$ here?
2d
comment Find all the zeros of $f(x) = x^3 + 3x + 5$ in $\Bbb Z_7$
Did you try plugging in values?
2d
comment Diagonal block matrices of a positive definite block matrix
Correct :) $\,\,\,$
2d
comment Diagonal block matrices of a positive definite block matrix
This should be relevant: math.stackexchange.com/questions/1221790/…
2d
comment Difficulty in Laurent series
The pole order is the (negative of) the most negative power in the Laurent expansion.
2d
comment Why can't you count up to aleph null?
@Timtech That's the thing. There isn't a "last" element here. There is a maximal element, but not a last. Last implies that you can reach that element in finitely many steps. "Last" is somewhat of a colloquialism.
2d
comment Why can't you count up to aleph null?
It seems to me that you want this to be an ordered set, but it does not really make sense to tack on $\aleph_0$ to the end in the way that you want.
Apr
27
comment Integral and Cauchy theorem
@george Someone else can fill in the details, but I pretty much gave a perfect guide to follow.
Apr
27
comment $\int^{2 \pi}_0 \frac{1}{ \sqrt{5}+\cos t}dt$, $\int^{2 \pi}_0 \frac{\cos^2t}{ 5-3\cos t}dt$ - Cauchy integral?
Write $$ \cos t = \frac{1}{2}\left(e^{it} + \frac{1}{e^{it}}\right)$$ and make the substitution $z = e^{it}$. You might also want to use a double angle identity on $\cos^2 t$ (not totally sure about that).