# Questions tagged [absolute-value]

For questions about or involving the absolute value function.

2,020 questions
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### Proof that there's a unique division quaternion algebra over a locally compact field?

There are many proofs that there is a unique division quaternion algebra over a locally compact field that is not $\mathbb{C}$. For instance this set of notes/book by John Voight contains two proofs: ...
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### How to solve equations with absolute value and using the Archimedean property

I'm trying to learn Real Analysis on my own, but I found that i'm a bit rusty with the elementary stuff. How do I solve equations like $|x| + |x+1| = 1$ and $|x-1| + |x+1| = 2$? I don't want the ...
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### Solving $\left| \frac{-2x-6}{4} \right| \le 5$ for $x$

Say I have a statement like: $$\left| \frac{-2x-6}{4} \right| \le 5.$$ And I want to find the closed interval form of $x$. i.e. I want to know what the maximum and minimum $x$ can be. How do I ...
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### Solving an equation with absolute values

The equation I am trying to solve is this : $\newcommand\abs[1]{|#1|}\abs{3y+7}=\abs{2y-1}$. My conventional approach is to split this into three intervals with $1/2$ and $-7/3$ being the two "split" ...
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### Proving Absolute Value Inequality

I had posted a portion of this earlier asking about how to interpret min(). I received some excellent answers, however, I have run into problems and feel stuck. I am posting the question in its ...
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### When should I put an absolute value sign around a function?

In Griffiths' introduction to QM book, I see $\int f^* f\ dx$ often written as $\int | f |^2 dx$, whereas $\int f^* g\ dx$ is understandably just that. Should I always write the absolute value sign ...