I have $ E \in \mathbb{R}^2$ such that $E=\mathbb{Q}^2 \cap {[0,1]}^2$. Is the boundary E : 1 open ? (no). 2.closed (yes) 3. compact (yes) 4.connected (no). 5 $E=bd E$ ?
the reason the commuting logic does not work for $\pi_1$ is because that [0, 1] has not enough dimensions to shift [0, 1] cup [1, 2] to [1, 2] cup [0, 1], however
Also, note that using the "more digits" option changes the numbers
and indeed continues to do so as you keep pressing it, getting closer and closer to the exact value (but still rather slowly). so presumably it's something to do with how WA actually does numerical summation in such cases.
In the text "Function Theory of One Complex Variable" Third Edition by Robert E.Greene and Steven G.Krantz. I'm having trouble proving the following case of the root test in $(1.)$
$(1.)$
$\text{Lemma 3.2.6 (The root test)}:$ The radius of convergence of the power series $\sum_{} a_{k}(z-P)^{...
Fractured my elbow a little bit today. Nothing serious but the pain meds might make me a little loopy. So if I start claiming the complex numbers can be ordered or spheres are Euclidean in terms of geometry please give me a little nudge. Other than that I just have to type one handed.
As for what I am doing during that scene in the dream, I was trying to find a counterexample of that theorem, which I suspect will involve drawing a right triangular prism in some weird topology so that such a line cannot be found anymore
Reality check will inform you that such theorem is too vague or incorrect
For example: That shape drawn there is really not a prism, because the base and the top don't match. It's more like some kind of frustum
and secondly, that vertical line drawn is not the height of this thing, rather it looks more like a median height or something
Given how we knew recently that my dreams is probably a Makov generator, it is kinda surprising such coherent nonsensical stuff can be generated from it
If this trend continues, perhaps eventually I can use my dreams to solve maths problems
Well then, in that case, you need to tell me what field are you take you questions on, so I can get myself ready if it is some unfamilar field
The cool thing about questions is that some of them are interesting enough that the discussion is more important than the answers, and I am looking forward to that
I'm 10 steps ahead of you. I'm a lack older than you are. You may be as smart as I am when you get to be my age, but you're not there now, so when I ask you a question you'll give me an answer
I suspect Twink somehow get affected by watching Judge Judy, and then proceed to immitate her. why I have no idea yet, I guess the video may contain clues...
https://en.wikipedia.org/wiki/Judge_Judy Sounds like a very elaborate prank attempt
I think if such thing happened next time, and the user don't explain what is going on (that it is a prank in motion), I think it will be flag worthy for chat disruption
Hmm, what qualifies as a constant function in a unit circle, the radius? If that way of thinking is correct, then this ODE system will solve into a torus of major radius 1 in the xt plane and minor radius $\omega$ in the yt plane
@TedShifrin I just spent some time reading Hirzebruch's talk at the 1960 ICM; he discusses Chern numbers of almost complex manifolds and gives an explanation of some theorems that Milnor apparently proved about them. I'm wondering whether you know what paper of Milnor describes these results (I don't think it's "On the Cobordism Ring $\Omega^*$ and a Complex Analogue, Part I" though it certainly involves cobordism).
In the text "Function Theory of One Complex Variable" Third Edition by Robert E.Greene and Steven G.Krantz. I'm having trouble proving the following case of the root test in $(1.)$
$(1.)$
$\text{Lemma 3.2.6 (The root test)}:$ The radius of convergence of the power series $\sum_{} a_{k}(z-P)^{...
