# Tagged Questions

For questions about or involving the absolute value function.

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### Compare difference between mean and actual

My problem is: I have two sets of numbers as follows: $X = {x_1, x_2, ..., x_n}; Y = {y_1, y_2, ..., y_m}$. Where $r$ is the actual value. $x^*$ is the mean of set X, $y^*$ is the mean of set Y, (n!=m)...
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### Close approximation for absolute value function

I made a very acurate approximation function for $\sqrt{n^{2}+1}$ It is $\sqrt{n^{2}+1}\approx\frac{2n(n^{2}+1)}{2n^{2}+1}+\frac{2n^{2}+1}{n(4(2n^{2}+1)^{2}+1)}$ From this I can make a very close ...
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### Automorphisms of local field

(1)Suppose that $K$ is a local field but not $\mathbb C$. Then show that any automorphism of $K$ is continuous. (We can assume that $K$ is $\mathbb R$ with classical absolute value or $K$ is a finite ...
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### Mixed Integer linear programming - absolute value of a variable not involved n the objective function

I'm looking to find the absolute value of the expression s-t. I have begun by introducing the following constraints: Where A is the absolute value. Unfortunately, A is not involved in the objective ...
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### Real Analysis Absolute values [closed]

Someone please help me with detailed explanation on how to solve this problem. For all $a, b \in \Bbb R$, show that; $$| a - b | \geq | a | - | b |$$
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### What are the solutions of $|x+y|=|x|+|y|$?

So I am having a problem in solving this type of equation. The problem I am dealing with is... $$\left|(2x-1) + \frac{3x-1}x\right| = \left|2x-1\right| + \left|\frac{3x-1}x\right|$$ Please help me ...
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### Does every non-Archimedean absolute value satisfy the ultrametric inequality?

The Archimedean property occurs in various areas of mathematics; for instance it is defined for ordered groups, ordered fields, partially ordered vector spaces and normed fields. In each of these ...
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### How to calculate the modulus of a complex number? [closed]

I know that for an equation of real numbers you could calculate the modulus as follows (if I am not mistaking): $$x = a + b$$ $$|x| = \sqrt{a^2+b^2}$$ But now I found this equation with this result:...
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### What region in $\mathbb{C}$ does $\left|{z-1}\right|+\left|{z+1}\right|$ = 2 describe?

I have played around with this a bit and keep getting something that doesn't seem right. Perhaps I'm overlooking something. Using the definition of distance in the complex plane I transform my ...
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### Why $|x|$ is not rational expression?

I'm 9th grade student, and my teacher said that $|x|$ is not rational expression ( expression like $\frac{p(x)}{q(x)}$ s.t $p(x)$ and $q(x)\neq 0$ are polynomial) but he didn't have convincing reason. ...
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### A basic inequality: $a-b\leq |a|+|b|$

Do we have the following inequality: $$a-b\leq |a|+|b|$$ I have considered $4$ cases: $a\leq0,b\leq0$ $a\leq0,b>0$ $a>0,b\leq0$ $a>0,b>0$ and see this inequality is true. However I ...
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### How to solve the differential equation $y'=y(1-y)$.

Up until now, we simply rearranged and integrated both sides, so $$y'=y(1-y)$$ $$\frac{dy}{dx}=y(1-y)$$ $$\frac{dy}{y(1-y)}=dx$$ $$\int\frac{dy}{y(1-y)}=\int dx$$ With partial fraction decomposition ...
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### generalised eigenvalue problem with absolute value

Problem: $\max_w |w^t A w|-|w^t B w|$ s.t $w^t C w=1$ If there was no absolute values, i.e. if the problem was $\max_w w^t A w-w^t B w$ s.t $w^t C w=1$ this would, by using the appropriate Lagrange ...