Tagged Questions

68 views

$\forall x \in \mathbb{R}$ show that $x=\sum_{n=1}^\infty k_na_n = \prod_{n=1}^{\infty}m_na_n$ …

Yet again, another cool problem from the book "problems in mathematical analysis" by Piotr & Witkowski: Prove that if $a_n \neq 0$, $n=1,2,\cdots$ and $\displaystyle \lim_{n \to \infty} a_n = 0$, ...
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Finding the coefficients of a partial differential equation after a change of coordinates.

I'm stuck in one of the mathematical steps of my physical problem. I've been following the derivation of my equations (starting at section 4) from this article Symmetric Euler-Angle Decomposition of ...
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Proving there are infinitely many integers having the identical set of prime factors.

Let positive integers $a$ and $b$, and let $a_0, a_1, a_2 \ldots$ where $a_i = a + b*i$ is the infinite arithmetic sequence they determine. Prove that there are infinitely many $a_i$ having the ...
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Sequent calculus - where should I start?

I am given this formulae. $A \land B \implies C \lor D \lor E$ I want to deduce this formulae with sequent calculus. But my problem is that I dont know where to start, or which rule to take first. ...
214 views

how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$

I am given this equation: $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$ I want to prove it: what i did is I take any $a \in f^{-1}(B_1 \cap B_2)$, then there is $b \in (B_1 \cap B_2)$ so ...
59 views

how to prove this: $f(A)=B$

I am given two sets: $A$ and $B$ and a function $f: A \rightarrow B$. I am asked to show and prove whether $f(A)=B$ is true or false. I am stuck not knowing how to do this. How can I do this?
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Exercise 1(d) from Courant

I'm having trouble understanding this "hint" in the back of (the first volume of) Courant's Differential and Integral Calculus text, which I'm just starting: One of the "challenging" Chapter 1 ...
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Proving there are no integer solutions for $3x^2=9+y^3$

Prove there are no $x,y\in\mathbb{Z}$ such that $3x^2=9+y^3$. Initial proof Let us assume there are $x,y\in\mathbb{Z}$ that satisfy the equation, which can be rewritten as $$3(x^2-3)=y^3.$$ So, ...
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$\log\left(\binom{n}{x} \pi^x (1-\pi)^{n-x}\right)=x\log \pi + (n-x)\log(1-\pi)\;\;?$

$$\log\left(\binom{n}{x} \pi^x (1-\pi)^{n-x}\right)=x \log \pi + (n-x)\log(1-\pi)$$ this is what i have. i dont understand how $\binom{n}{x}$ disappears, but the rest is fine. I tried this, but it ...
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complex numbers - proof of this statement

i am trying to prove this statement, i dont but how to start. $$\forall z,w \in \mathbb{C}\quad |z|^2+|w|^2=\frac{1}{2}(|z+w|^2+|z-w|^2)$$ can someone please show me how start?