Talk:Absolute value

message: 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)
thread_title:  Absolute number listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: I have just seen the equation |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, \max(a, b) = \begin{cases} a, & a \geq b \\ b, & a < b \end{cases}, so that one only has to define one of |\ | and \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)
thread_title:  Absolute value as a maximum 

message: From -a <= x <= a, we would have x = a and x = -a, a contradiction. Maybe the intention was to write: 
|x| < a iff -a < x < a.
I never saw a book that explains this equivalences. I mean, though intuitive, what is the logical justification why we get the logical "and" in a situation and the logical "or" in another? For example:
|x| = a iff x = a or x = -a
|x| < a iff x < a and x > -a
|x|> a iff x > a or x > -a
The explanation I gave to myself is that the definition of abs is equivalent to:
(x>=0 and |x| := x) or (x<0 and |x| := - x).
For example |x| < a iff 
(x >= 0 and x < a) or ( x < 0 and -x < a).
And then it's just interval calculations and distributions of logical operations. Sr cricri (talk) 18:32, 2 April 2023 (UTC)
replies: text: Perhaps rather than trying to convince us by drawn-out explanations you could provide an explicit example of two numbers x and a for which |x|\le a but not -a\le x\le a. If you could do that, it would make for a more convincing argument. —David Eppstein (talk) 18:36, 2 April 2023 (UTC)
replies: text: Oh, I see now, you are right David. I didn't see that |x| <= a is  x < a or x = a. Maybe it is better to delete this topic discussion. Sr cricri (talk) 18:56, 2 April 2023 (UTC)
thread_title:  |x| <= a doesn't imply -a<= x <= a 

message: "In mathematics, the absolute value or modulus" - are these terms equal or does it depend on context?
This discussion came up in a stack overflow thread which referenced this article as evidence that absolute value = modulus. However, some additional reading suggests that these may not be entirely interchangeable terms, perhaps making this article a source of misinformation. It's been about 20 years since my last math class, so I'm hoping someone more familiar with this subject matter might be able to clarify this as it is causing discussion and confusion elsewhere:
https://stackoverflow.com/questions/664852/which-is-the-fastest-way-to-get-the-absolute-value-of-a-number
https://math.stackexchange.com/questions/472856/what-is-the-difference-between-modulus-absolute-value-and-modulo Oudent (talk) 05:36, 18 July 2023 (UTC)
replies: text: This is going to depend on some specific source's precise definitions. As with most things of mathematics, conventions are not entirely standardized and vary a bit from country to country, year to year, source to source. Some sources surely treat these as interchangeable synonyms. Other sources might use "absolute value" for real numbers and "modulus" for complex numbers, vectors, matrices, or other kinds of quantities. This article seems fine though. –jacobolus (t) 06:14, 18 July 2023 (UTC)
thread_title:  Absolute Value = Modulus? Is this entirely accurate?