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Jul
27
comment Find a plane with distance $3$ from $3x-y-z = 0$
@Mr.Fry your comment is definitely correct and it seems to me to be the best way to approach this problem. In fact for this example we can choose $P=0$ and then it is quite easy to calculate an equation for the plane (i also checked that the equation agrees with the current answer, which has 3 upvotes already)
Jul
27
comment Find a plane with distance $3$ from $3x-y-z = 0$
@Mr.Fry why not just post your comment as an answer?
Jul
26
comment Intuition for the Cauchy-Schwarz inequality
@IttayWeiss I'm really thinking about vectors in $\mathbb{R}^n$ here. In this case $\theta$ has a clear meaning without CS and one can prove the above formula using the law of cosine's (as I'm sure you know). I just finished teaching calc 3 so I got into the habbit of thinking concretely about some of these things.
Jul
26
answered Intuition for the Cauchy-Schwarz inequality
Jul
25
revised Using Green's theorem to find an area.
added 4 characters in body
Jul
25
comment Using Green's theorem to find an area.
Thanks, you can upvote and/or accept this answer if you'd like.
Jul
25
revised Using Green's theorem to find an area.
added 141 characters in body
Jul
25
answered Using Green's theorem to find an area.
Jul
25
comment Why is $\phi : \operatorname{Hom}(\mathbb{Z},G) \to G$ given by $ f \mapsto f(1)$ surjective?
The idea is we "try" to do it and then check that it actually works. If $f(1)=g$ then by the homomorphism property $f(n)=g^n$ for any integer $n$. So we just take this to be the definition of the map, and then we need to check that it is well defined. In other words if $n=m$ then we need that $g^n=g^m$. But of course this is true for any integers $n$ and $m$.
Jul
25
revised Why is $\phi : \operatorname{Hom}(\mathbb{Z},G) \to G$ given by $ f \mapsto f(1)$ surjective?
added 3 characters in body
Jul
25
answered Why is $\phi : \operatorname{Hom}(\mathbb{Z},G) \to G$ given by $ f \mapsto f(1)$ surjective?
Jul
23
answered Find Total Mass of a Solid
Jul
23
revised Volume of Region Paraboloids
added 2 characters in body
Jul
23
comment Volume of Region Paraboloids
Well start by finding the antiderivative of $r$ with respect to $z$ ($r$ is constant here). Then you need to evaluate at the limits of integration before you do the next 2 integrals.
Jul
23
comment Volume of Region Paraboloids
Yup, that looks right!
Jul
23
answered Volume of Region Paraboloids
Jul
15
comment Why do we require differential manifolds to be Hausdorff?
Connected is not usually a requirement for a smooth manifold.
Jul
13
comment Representation of an abelian group
Ok, well good luck. I don't know what results you have proven in class so I don't think I can help.
Jul
13
comment Representation of an abelian group
@john Have you proven that characters on any subgroup extend to characters of the group? Using this result you can generate a cyclic subgroup of $x$, define a character on this cyclic subgroup as explained in my answer, and extend to a character $\chi$ such that $\chi(x)\neq 1$ as desired.
Jul
12
comment Representation of an abelian group
This argument leaves off the one part of the proof that really needs justification. This is the part that my answer explains.