# Talk:Absolute value

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WikiProject Mathematics (Rated B-class, Mid-priority)

@Paul August: The repeated, deteriorating edits by Karjam and the (linguistic) improvement by Macrakis brought me to focus on the root of the desire for an additional reasoning - the definition, thereby rendering superfluous any ex-post explanation of why the given property does hold.

I am strongly convinced that Karjam's (and his cohort's) view, on "cancelling out" (it's really called this) two minuses being a preferable and sound enough reasoning, is based on a general flaw in elementary math education, considering this "rule" as heaven sent, and not as a provable property in the setting of ubiquitous numbers. One consequence of this inconsiderate "two minus cancel" is, imho, also the reason for not easily accepting the bi-valent introduction of ${\displaystyle i}$ by ${\displaystyle i\cdot i=-1}$, as opposed to ${\displaystyle (-1)\cdot (-1)=1\cdot 1=1}$, and preferring (for purely historical reasons?) ${\displaystyle i={\sqrt {-1}}}$, rather vague, if not undefined, at the time of introducing ${\displaystyle i}$.

I was even tempted to replace the definition in this article by

${\displaystyle |x|={\begin{cases}(+1)\cdot x,&{\mbox{if }}x\geq 0\\(-1)\cdot x,&{\mbox{if }}x<0,\end{cases}}}$

but imagined this to have no chance under WP-community's supervision. Thanks for asking.

P.S. to any passer-by: I'd like to know about possibilities to substitute "\phantom" in WP. Thanks. Purgy (talk) 08:45, 3 December 2017 (UTC)

Safe to say, my own explanations does not take into account complex numbers. Not that it's meant to, seeing as though it's meant more for the phenomena of real numbers rather than those imaginary.
I can now see what you about my explanation being flawed, however, seeing as though absolute value also has applications within that field. --Karjam, AKA KarjamP (talk) 10:01, 3 January 2018 (UTC)

## On the first ...

... line of this wikipedia article: " x, |x| = −x for a negative x" Is simply not true, i would like to have edited it myself but i do not know the mathematical language used in this article. It should of course be |-x| = x =) — Preceding unsigned comment added by Vrkiller (talkcontribs)

No, if x = -2, then |x| = |-2| = 2 = -(-2) = -x. Paul August 20:00, 19 December 2018 (UTC)

## Absolute number listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Absolute number. Please participate in the redirect discussion if you wish to do so. — Arthur Rubin (talk) 10:43, 19 May 2019 (UTC)

## Short description

@D.Lazard: The purpose of a short description is to aid disambiguation, not to be a comprehensive mini-definition of the subject. Sometimes mini-definitions can work, but in this case it'd require going over the 40-character target (the previous description was 60 characters). {{u|Sdkb}}talk 19:49, 14 May 2021 (UTC)

"Concept" is even shorter and is almost as useful as "Mathematics concept". Moreover, "Mathematics concept" is gramatically dubious and, in any case, ambiguous: it may mean "concept of mathematics" or "concept in mathematics", but certainly not "concept used in mathematics" which seems to be the intended meaning. Also, the limit of 40 characters is a recommendation, not a policy.
This being said the current formulation is not very good, not because its number of characters, but because it is too cumbersome. I'll try for a better formulation. D.Lazard (talk) 20:35, 14 May 2021 (UTC)
Another possibility might be "distance of a number from zero" (30 characters). —David Eppstein (talk) 20:56, 14 May 2021 (UTC)
I like that a lot. {{u|Sdkb}}talk 21:09, 14 May 2021 (UTC)
Me too. Paul August 00:58, 15 May 2021 (UTC)
Before reading David's suggestion, I have changed the sd into "Magnitude of a possibly negative number" (39 character). IMO, the two versions are acceptable. I have thought to a version using "distance", but I have rejected it because this use of "distance" may be confusing for a non-mathematician. Another reason of my choice is that it emphasizes that the absolute value makes sense only if non-positive numbers are considered. I'll not be bothered if there is a consensus for David's version. D.Lazard (talk) 08:50, 15 May 2021 (UTC)

## Absolute value as a maximum

I have just seen the equation ${\displaystyle |x|=\max(x,-x)}$ and I am absolutely baffled that I had not come across this until now! Surely this should be included somewhere in the article, as it is much more compact than the piecewise definition – indeed it "piggybacks" off of the piecewise definition of the maximum, ${\displaystyle \max(a,b)={\begin{cases}a,&a\geq b\\b,&a, so that one only has to define one of ${\displaystyle |\ |}$ and ${\displaystyle \max(\ ,)}$ by a piecewise formula, not both. The fact that this formula is not in the article suggests to me that many other people also have not seen this property (of course it's obvious once you have seen it, but without seeing it most people wouldn't think of it). Joel Brennan (talk) 22:26, 18 April 2022 (UTC)