RESULT 1: If $I_1, I_2,..., I_n$ are disjoint open intervals and $E$ is a bounded set such that $E \subset \cup_{k=1}^n I_k$ then $m^*(E)=\sum_{k=1}^n m^*(E \cap I_k)$. (where $m^*(S)$ is the Lebesgue outer measure of $S$.)
RESULT 2: If $\{I_k\}_{k=1}^\infty$ is a disjoint collection of open int...
I don't have to calculate the curvature at a given $x$, I have to find a general expression.
For most curves, that's impossible, in the sense that the definition I mentioned above is the most you can get. So I don't know if I'm missing something important, since the exercise makes no sense.
Maybe the point of the exercise is "see? curvature is hard to calculate".
A student takes a true-false examination containing 20
questions. On looking at the examination the student and that he
knows the answer to 10 of the questions which he proceeds to answer
correctly. He then randomly answers the remaining 10 questions. The
instructor selects 2 of the questions at...
if you have an infinite collection of disjoint intervals in a bounded set, the lengths of the intervals and the distances between them must get arbitrarily small
thus the separation property guarantees the covers are finite
Well, to prove $\geq$, just prove that, given any covering $L$, there's a finer covering $L'$ such that $(L'\cap A)\cap(L'\cap B)=\emptyset$. I think that suffices, but I may be wrong.
Ohh ... It would mean that your fourth line meets the surface in 3 points, and hence is in the surface. The fourth line was supposed to be in general position.
Hello, if I have $F' = (P(x)\phi(x))' = P'(x)\phi(x) + P(x)\phi(x)'$ where P(x) is a polynomial of degree n, what would be the derivative if I have to do $F' = (\frac{P(x)\phi(x)}{Q(x)})'$
thanks, its actually a question in functional analysis. I am to show that $\phi(x) = \frac{-1}{1 - |x|^2}$ if $|x| < 1$, 0 if $|x| \geq 1$ is a function that belongs to the space $C_0^\infty$, ie the set of all continuous, infinitely differentiable functions SUCH THAT the support is COMPACT.
so sorry, now i have a polynomial of degree 3n - 2 and another polynomial Q with degree 2n so I am try to prove it is infinitely many times differentiable by induction.
@PeterTamaroff how long was it? Maybe I can go back up in chat to look at what you said
@Twink: I have known measure theory, but it's basically my least favorite part of analysis. Lebesgue integrals are fine :) plenty of people here who know it better than I.
@Emrakul There is one by I.M Yaglom called Convex Figures
@Emrakul However, generally books of this style are very out of fashion. My personal recommendation is when reading a book read the theorem and cover up the proof, try to prove it yourself, if you cant get it, read a line of the proof, try to prove again, etc
Speaking of books, does anyone know of a book about the more exotic number?
Such as transcendental numbers, non computable irrationals, transfinite numbers, etc.
Im looking for something that is a little bit rigorous, not a general-public level book
I just want to let you know; I find <the chained ring> in a research a bout the complement of zero-divisor graph of commutative rings
4 hours later…
user87637
11:40
@Ethan You should really apply to UCLA since it is close to your home and it is a top school in mathematics. Also, look at the curriculum to see if you like it as for your other choices, and the cost of living and things like that.
@FernandoMartin Ok so I have the following matrix: $ A=\begin{pmatrix} a & b \\ c & d \end{pmatrix} $ and I am being asked to show that using conjugation by elementary matrices, one can "eliminate" the a entry.
