my math question is how do you get 1428 out of 1,2,6, and 8 using only each digit once
I need the answer by September 12,2014 or I will be disqualified from school
jajaa ok ok @hippalectron, seems complicated my first idea was to use something similar to the discrete topology but of course immediately I realize that the idea doesnt work because might have to generate the same topology but makes the space complete....
@JohnDoe But, one would have to download the pdf etc. It's nonzero work to do. More effective to scare me off is the name Galerkin appearing. I strongly disliked that stuff when I knew it, now I'm not in the least inclined to dig into it.
@MikeMiller What are $0$ and $1$ as elements of $\mathbb{R}^2$? Identify with $\mathbb{C}$?
Hi, I have a few differential equations questions. First off I have a problem named as such: The field mouse population is modeled by the equation: $\frac{dp}{dt} = 0.5p-450$ My first question is what exactly is $\frac{dp}{dt}$ represent? I know it is basically the derivative of $p$ with respect to time, but does this mean it is the rate at which the population grows...? Can someone explain exactly what the equation is modeling and why? Especially why we use $0.5p$ instead of $0.5t$?
@MikeMiller I have found a relevant paper which proves that if $R$ is commutative and that the semigroup $R^\times$ is finitely generated then $R^\times$ is finite.
@JoseAntonio Take a continuous function $f\colon \mathbb{R}\setminus \{0,1\}\to\mathbb{R}$, and consider $\Gamma(f) = \left\{ (t,f(t)) : t\in \mathbb{R}\setminus\{0,1\}\right\}$. The graph $\Gamma(f)$ inherits a metric from $\mathbb{R}^2$, and transporting that back, you get a metric on $\mathbb{R}\setminus\{0,1\}$ inducing the standard topology. Now you need to choose $f$ so that $\Gamma(f)$ is a closed (hence complete) subset of $\mathbb{R}^2$.
@JohnDoe Well, there's $\{0\}$. And if you don't require the space to be Hausdorff, there can also be nontrivial bounded linear subspaces. But for Hausdorff TVSs (over $\mathbb{R}$ or $\mathbb{C}$), the trivial is the only bounded linear subspace.
I think there is too much worry about those kids that come here for having the homework problems solved. If I were a professor I wouldn't see how MSE would possibly help any of them if they only want to cheat. Just think about it! You go to school with the lessons that are done here, but what's next? In a real test you fail!
@Chris'ssis: You need mental visualization of the problem. Some get that through doing the math themselves, some get that through visualization, some get that through discussion and being taught
Actually disregarding my last question, is this the proper way to integrate this? $\int\frac{dp}{0.5p-450} = 2\int\frac{dp}{p-900} = 2ln|p-900|$ however my professor says it should be: $2ln|0.5p-450|$ where am I going wrong?
Hmm.. let me try and work it out.. $\int\frac{dp}{0.5p-450} = \int\frac{dp}{0.5(p-900)} = \int\frac{1}{0.5}\frac{dp}{(p-900)}= \int2\frac{dp}{(p-900)}=2\int\frac{dp}{(p-900)}=2ln|p-900|+C$
So where did I go wrong in this? It seems to be right, but evidently not.
@Alizter We want to prove that $\exists k$ such that there is an $x$ such that $2^x \in [n^{2^k}, (n+1)^{2^k}]$. Consider the interval $[\log_2(n), \log_2(n+1)]$.
Cutoff the two ends of the interval to produce an interval $[a/b, a'/b']$, (which is possible as $\Bbb Q$ is dense in $\Bbb R$) with rational limit points $a/b, a'/b'$. There exists an integer $y = bb'x$ inside $(ab'2^k, a'b2^k)$ for some appropriate choice of $a/b$,$a'/b'$ and $k$. Hence, $x/2^k \in (a/b, a'/b') \subset [\log_2(n),\log_2(n+1)]$. $\blacksquare$
Actually, @Alizter, you can just work your way though $[a/b \cdot 2^k, a'/b' \cdot 2^k]$ for some large enough $k$ to make $\lfloor a/b2^k \rfloor$ and $\lfloor a'/b' 2^k \rfloor$ differ as much as possible to fit an integer between those two.
Nonetheless, the whole problem is about proving that rationals with denominators a power of $2$ are dense in $\Bbb Q$, which is obvious/elementary/easy.
@Alizter now you can use this fact to prove that any nonempty set $S$ of positive nonzero integers such that if $x \in S$ then $\lfloor x \rfloor$ and $4x$ are in $S$ is all of $\Bbb N \setminus \{0\}$
@DanielFischer The phone company informed me that they're upgrading my internet service from 3 Mbps to 18 Mbps. They're getting rid of the old DSL service.
damn I get stuck again with the problem of how to find a complete topology for the linea without two poins. Someone knows a source to find similar problems. Sorry but we´ve seen in class very slightly the concept of topology and I'm crush trying to do the exercises in the book.
@DanielFischer first of all sorry for being annoying. Second with respect to your big hint, (I´m talking to the problem of a metric to make R \{01} complete and with th same topology as the relative topology) is not necesary that the map f: R \{01} \to R also tis inverse has to be continuous? sorry if is a stupid question...
Wikipedia and this book say the local truncation error of Euler method is $O(h^2)$. But this book and A friendly Introduction to Numerical Analysis say it's $O(h)$. Which is correct? I have a similar problem with implicit trapezoidal method.
EDIT
My numerical investigation shows that the LTE of...
@JoseAntonio You use $f$ to get a map $g\colon t \mapsto (t,f(t))$. And $g$ is the homeomorphism. $g$ is continuous if and only if $f$ is, and the inverse of $g$ is the restriction of a coordinate projection, hence continuous (whatever $f$ is).
Anyone have any good resources for 3d differential geometry?
Links, and whatnot.
I can't find anything "nice" on calculating the curvature of a point on a 3D surface. I have been able to make a mental flow chart by looking through wikipedia, though nothing spectacular enough to appreciate what is happening.
The big thing has nothing to do with multivariable, it is more general. The only truly(?) multivariable thing needed is that the coordinate projections are continuous.
my math question is how do you get 1428 out of 1,2,6, and 8 using only each digit once
I need the answer by September 12,2014 or I will be disqualified from school
Wikipedia and this book say the local truncation error of Euler method is $O(h^2)$. But this book and A friendly Introduction to Numerical Analysis say it's $O(h)$. Which is correct? I have a similar problem with implicit trapezoidal method.
EDIT
My numerical investigation shows that the LTE of...
