@NotNotLogical in any case, the short answer to your question is, many big-list questions are closed because they are seen as off topic by the community.
by nature big-list is off topic here, but exceptionally good ones are allowed to stay around as exceptions. the community didn't feel yours was well-defined enough.
Okay, I just wanted to be sure because I recently came across $\sum^{\prime}$ and thought the prime was just an artifact of some old typesetting, but I was wrong
Let $E$ be a topo space, $A \subset E$ & let $a$ be a cluster pt of A. Then a map $f$ of $A$ into a Hausdorff spc $E'$ has at most one limit at the point $a$ wrt $A$.
What does wrt $A$ mean here?
with respect to, but what does that mean here?
Ah, the book says $\lim_{x \in A, x \to a}$
makes sense
In a Hausdorff space $E$ every finite subset is closed.
For any $x \in E\setminus A$, take the intersection of all open sets $U_i$ disjoint from $a_i \in A$.
that contain $x$
Then it's disjoint from $A$ and open so $E\setminus A$ is open
ok, the integral is $$\frac{1}{\left(z^2+x^2\right)^(3/2)}
and I have to integrate it w.r.t x
I tried differentiating it first and a few substitutions but couldn't get it to work.
I tried substituting u = z^2+x^2; u=x^2 and some others but neither of them worked. And I also tried differentiating $$\left(z^2+x^2\right)^(1/2)$$ to see if I could sort of "work it backwards" but they didn't work out, and I am a bit stumped how else to approach it.
If, $a+b+c+abc=4$, with $a,b,c$ being positive reals, then prove or disprove the following inequality: $$\frac{a}{\sqrt{b+c}}+\frac{b}{\sqrt{a+c}}+\frac{c}{\sqrt{a+b}}\geq\frac{a+b+c}{\sqrt2}$$
ok so I tried substituting $$x=z\tan\theta$$ and the integral reduced to $$\frac{1}{z^2\left(1+\tan\theta\right)^{3/2}}\frac{1}{1+\theta^2}d\theta$$, am I on the right track?
If $G = R \times H$ where $H$ is the multiplicative group of the ring $R$, then $R$ seems to be isomorphic to the subset $\{(\phi(r), \psi(r))\}$ where $\phi(r) = (r, 1)$ and $\psi(r) = (0, r)$, except $1 = 0$ in that set.
Guys, do you think it's reasonable to study maths, if I'm mediocre at it? I always loved it, but now at college I've realized how much I suck at it and I am not sure if my life is going in the right direction, which kinda depresses me :(
@BoniTea I spent many hours studying series, and in the test, I made a sequence of stupid mistakes failed it. Some people are natural, on the other hand. I am not. Those thing are very demotivating :/ How do you stay motivated?
@PoliTolstov I'm sure you can :) I have two balls (you know what I mean) made from different materials. Induced electric dipole in one is 1.5 times smaller than in the other. I am given electric permitivity of one of them and am supposed to find permitivity of the other... So I guess the question is how is polarizability connected with permitivity
