# All Questions

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### Formula or function to generate a score between 1 to 10 based on 2 factors.

I'm conducting a model auction as part of an event at my college. 25 teams would be participating and I need to give scores to each of them to decide the five highest scoring teams to promote them to ...
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### Different ways of representing a second cohomology class

There are probably many ways of talking about a second (integral) cohomology class of a smooth, closed, orientable manifold $M$ of dimension $n$. Here are a few, with $\alpha\in H^2(M,\mathbb{Z})$: ...
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### Do these axioms fully describe the integers?

Here, I use Peano-like axioms to describe the set of integers $Z$. They are based on two successor functions, each starting with a common point of $0$, and a principle of induction for the integers. ...
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### “Question about measure theory” [closed]

If $f\in M^{+}(X,$ X $)$ and $\int f\, d\mu<{\infty}$, then the set $N = \{x\in X: f(x)>0\}$ is $\sigma$-finite (that is, there exists a sequence $(F_n)$ in X such that $N \subset \bigcup F_{n}$ ...
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### Can you prove why Popsicle Stick Multiplication works?

This is a unique way of multiplying numbers by using sticks. Let's call it "Popsicle Stick Multiplication". Or maybe "Linear Algebra" quite literally. Take a look at both images that I've drawn ...
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### Exterior, Interior, Boundary

If we denote the general point of $\mathbb{R}^2$ by $(x,y)$, determine $\operatorname{Int}A$, $\operatorname{Ext}A$, and $\operatorname{Bd}A$ for the subset $A$ of $\mathbb{R}^2$ specified by each ...
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I’m looking for an informal and intuitive explanation of the Borel-Cantelli Lemma. The symbolic version can be found here. What is confusing me is what ‘probability of the limit superior equals $0 ... 2answers 75 views ### What are the sets of integers obtained from multiplication/division from a given set of primes called? We are given some (finite) set of primes$P=\{p_1, p_2, \ldots, p_n\}$. Define the following two sets:$S$is the set of all integers that can be generated from$P$by multiplying members of any ... 2answers 1k views ### Dirac Delta Function as Initial condition for 1D Diffusion PDE: ONE or TWO equations(conditions)? I have 1D diffusion (u(t,x)) PDE with Dirac Delta initial condition. Question is regarding it's implementation: Dirac delta func is formally defined as an encapsulation of 2 conditions: 1st ... 7answers 5k views ### How to read a book in mathematics? How is it that you read a mathematics book? Do you keep a notebook of definitions? What about theorems? Do you do all the exercises? Focus on or ignore the proofs? I have been reading Munkres, Artin, ... 3answers 147 views ### a problem in geometric probability Inside a square of side$2$units , five points are marked at random. What is the probability that there are at least two points such that the distance between them is at most$\sqrt2$units? ... 1answer 64 views ### Four times the distance from the$x$-axis plus 9 times the distance from$y$-axis equals$10$. What geometric figure is formed by the locus of points such that the sum of four times the distance from the$x$-axis and nine times its distance from$y$-axis is equal to$10$? I get ... 2answers 978 views ### Classify groups of order 27 Let$|G|=27$. Prove that all subgroups of index 3 are normal. Classify all groups of order 27. I can do the first one, but the classification is overwhelming. I don't even know where to start. ... 2answers 47 views ### Is my answer correct to this homework involving sets? Of a group of people, each person is wearing green, blue, or both. One-fifth of those wearing green are also wearing blue. One-eighth of those wearing blue are also wearing green. Are more than ... 4answers 398 views ### Is there an abbreviation for “almost all$x\in X$”? Is there an abbreviation for "almost all$x\in X$? I have "$\forall a.e. x\in X$" in my mind, but i see nobody uses this.. 2answers 428 views ### Why should Gaussian noise have fractal dimension of 1.5? In a paper I'm trying to understand, the following time series is generated as "simulated data": $$Y(i)=\sum_{j=1}^{1000+i}Z(j) \:\:\: ; \:\:\: (i=1,2,...,N)$$ where$Z(j)$is a Gaussian noise with ... 1answer 411 views ### Finding the equation of a line entirely defined by a three variable equation. How can you find the equation of a line that lies completely in a set defined by a three variable equation. For instance, the equation of a line entirely in the set defined by$x^2 + y^2 - z^2 = 1$... 0answers 52 views ### The$I$-torsion submodules of an injective module [duplicate] Possible Duplicate: Prove that the following module is injective Prove that$I$-torsion submodules of injective modules are injective (the ring is Noetherian). Please help me. 1answer 3k views ### When does Schwarz inequality becomes an equality? In Spivak Calculus you are asked to prove that in Schwarz inequality, equality holds only when$y_1 = y_2 = 0$or when there is a number$\lambda$such that$x_1 = \lambda y_1$and$x_2 = \lambda ...
Solve the equation below. $$x^2+\frac{81x^2}{(9+x)^2}=40$$ I couldn't solve it after trying many time.