# All Questions

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### How to show A={q belongs to X ; p belongs to X, d(p,q)>delta, delta>0} is closed?

first of all, i used "belongs to" to mean that p is an arbitrary element of X i tried it directly and take A's complement and show it is open but failed to both way i know when union boundary of ...
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### How to calculate $f(n)=1\binom{n}{1}+2\binom{n}{2}+3\binom{n}{3}…n\binom{n}{n}$

$$f(n)=1\binom{n}{1}+2\binom{n}{2}+3\binom{n}{3}.....n\binom{n}{n}$$ Is there a formula for this?
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### Prevent Maple to evaluate before simplify a function

I have been trying to find a domain of $f(x)=\frac{x}{\frac{(x+2)}{(x-3)}}$ using different kind of software ( its clear the domain of this function is $\mathbb{R}\backslash \{-2,3\}$ ). When I tried ...
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### Is there a known method for finding extremely huge squarefree numbers?

People often compete to beat the record for largest known prime (it is currently $2^{57,885,161}-1$). There are also big money prizes for finding explicit prime numbers exceeding specific magnitudes. ...
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### Prove that $E(\mathbb{C})^{\text{tor}} \cong \mathbb{Q}/\mathbb{Z} \times \mathbb{Q}/\mathbb{Z}$.

Let $E$ be an elliptic curve over $\mathbb{C}$. We know that $E(\mathbb{C}) \cong \mathbb{C}/L$ (this is a group isomorphism) for some lattice $L \subset \mathbb{C}$. Using this fact prove that ...
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### Why is $\hat{x}$ in the linear regression equation $A^TA\hat{x} = A^Tb$ part of $C(A^T)$

When finding the best fit line for a number of points, we use $A^TA\hat{x} = A^Tb$ where we solve for $\hat{x}$. I understand that the projection $p=A\hat{x}$ is part of the column-space of $A$ and ...
A few month ago I had to prove $\lambda(\mathbb{Q}) = 0$ (where $\lambda$ is the one-dimensional Lebesgue measure). The idea: Let $\varepsilon \gt 0, r_n := \frac{\varepsilon}{2^n}$ and $\mathbb{Q} = ... 0answers 6 views ### Zooming views relative to point I'm making a viewer for a fractal generated by convergence to a root of some polynomial using a root finding algorithm. (Examble fractal) in the complex plane. I then made an interactive viewer, ... 1answer 11 views ### Exponential generating function for number of 10 length sequences built from the alphabet, with some restrictions I've got the following homework question. If anybody could possibly point me in the right direction, that would be great: Suppose X is a sequence with 10 terms built from 26 letters {a, b, c, ..., ... 0answers 48 views ### How to solve this integral ($\int _{\frac{\pi }{6}}^{\frac{\pi }{4}}\sqrt{1-\tan ^2\left(x\right)}dx\$)
$$\int _{\pi/6}^{\pi/4}\sqrt{1-\tan ^2\left(x\right)}dx$$ Hey, can you help me to solve this integral please? Thanks.