Question

Can the function $\max(x,y,z)$ be expressed in terms of absolute values (not nested)?

score 144 · Answer 1 · 2023-03-01 18:43:04

144

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Can the function $\max(x,y,z)$ be expressed in terms of absolute values (not nested)?

Published on 01 Mar 2023 - 18:43

score 119 · Answer 2 · 2026-03-26 09:48:30

119

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Two approaches to change the absolute value in Linear Programming

Published on 26 Mar 2026 - 9:48

score 48 · Answer 3 · 2026-03-28 03:32:53

48

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How deeply nested can absolute values be, without being denestable?

Published on 28 Mar 2026 - 3:32

score 47 · Answer 4 · 2023-03-07 19:10:20

47

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A (classical) bound on the jumps of a cadlag function: $\left|\Delta f(t)\right|\leq 2\,\sup_{0\leq s\leq t}\left|f(s)\right|$.

Published on 07 Mar 2023 - 19:10

score 36 · Answer 5 · 2023-03-08 09:50:26

36

Views

Absolute value having $4$ distinct solutions

Published on 08 Mar 2023 - 9:50

score 68 · Answer 6 · 2023-03-09 14:51:27

68

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Difference between $x/|x|$ and $|x|/x$

Published on 09 Mar 2023 - 14:51

score 288 · Answer 7 · 2023-03-11 03:37:45

288

Views

Absolute value and $\pm$ sign problems in solving $\frac{\mathrm{d}y}{\mathrm{d}x}=y\left(1-y\right)$

Published on 11 Mar 2023 - 3:37

score 330 · Answer 8 · 2026-03-25 22:26:43

330

Views

Conflicting results for $\int\frac{|x+1|}{x}\,\mathrm dx$

Published on 25 Mar 2026 - 22:26

score 63 · Answer 9 · 2023-03-12 16:50:28

63

Views

Improper Integral which should diverge

Published on 12 Mar 2023 - 16:50

score 98 · Answer 10 · 2026-03-26 02:57:54

98

Views

Understanding a proof that, if $|a-1|+|b-1|=|a|+|b|=|a+1|+|b+1|$, then the minimum value of $|a-b|$, over distinct reals $a$ and $b$, is $2$.

Published on 26 Mar 2026 - 2:57

score 87 · Answer 11 · 2023-03-28 05:19:45

$\DeclareMathOperator\isZero{isZero}$ Proving $isZero(x) = 1 - \frac {x^2 + 1 - (|x + 1|) (|x - 1|)}{2}$ for $x < 0$ and $ x > 0$ (x is an Integer)

score 26 · Answer 12 · 2023-03-28 18:59:47

26

Views

An upper bound for $ \min _{\sigma \in S(k)}\left\{\sum_{j=1}^{k}\left|w_{\sigma(j)}-v_{j}\right|\right\}$

Published on 28 Mar 2023 - 18:59

score 64 · Answer 13 · 2026-03-28 12:02:45

64

Views

Presentation of $(xy)$ as a $\mathbb{Z}[x,y]$-module.

Published on 28 Mar 2026 - 12:02

score 101 · Answer 14 · 2026-03-26 02:54:25

101

Views

JS Milne Algebraic Number Theory 8.6 : normalized absolute values for local fields

Published on 26 Mar 2026 - 2:54

score 45 · Answer 15 · 2023-03-31 07:29:04

If $a, b, c, d \in \Bbb R$ and $ab+cd, ad+bc \neq 0$, prove $\vert(a^2+b^2-c^2-d^2)/(ab+cd)\vert \lt 2 ⇒\vert(a^2-b^2-c^2+d^2)/(ad+bc)\vert \lt 2$

List Question

Can the function $\max(x,y,z)$ be expressed in terms of absolute values (not nested)?

Two approaches to change the absolute value in Linear Programming

How deeply nested can absolute values be, without being denestable?

A (classical) bound on the jumps of a cadlag function: $\left|\Delta f(t)\right|\leq 2\,\sup_{0\leq s\leq t}\left|f(s)\right|$.

Absolute value having $4$ distinct solutions

Difference between $x/|x|$ and $|x|/x$

Absolute value and $\pm$ sign problems in solving $\frac{\mathrm{d}y}{\mathrm{d}x}=y\left(1-y\right)$

Conflicting results for $\int\frac{|x+1|}{x}\,\mathrm dx$

Improper Integral which should diverge

Understanding a proof that, if $|a-1|+|b-1|=|a|+|b|=|a+1|+|b+1|$, then the minimum value of $|a-b|$, over distinct reals $a$ and $b$, is $2$.

$\DeclareMathOperator\isZero{isZero}$ Proving $isZero(x) = 1 - \frac {x^2 + 1 - (|x + 1|) (|x - 1|)}{2}$ for $x < 0$ and $ x > 0$ (x is an Integer)

An upper bound for $ \min _{\sigma \in S(k)}\left\{\sum_{j=1}^{k}\left|w_{\sigma(j)}-v_{j}\right|\right\}$

Presentation of $(xy)$ as a $\mathbb{Z}[x,y]$-module.

JS Milne Algebraic Number Theory 8.6 : normalized absolute values for local fields

If $a, b, c, d \in \Bbb R$ and $ab+cd, ad+bc \neq 0$, prove $\vert(a^2+b^2-c^2-d^2)/(ab+cd)\vert \lt 2 ⇒\vert(a^2-b^2-c^2+d^2)/(ad+bc)\vert \lt 2$

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