Talk:Inequation

message: "In mathematics, an inequation is a statement that two objects or expressions are not the same."
I almost choked, reading that.  An equation is a *problem*, which consists in finding the (any, all) value(s) some unknown entity may have if some equality is to be satisfied. 
Accordingly, an inequation is a problem, which consists in finding the (any, all) value some unknown entity may have if some inequality is to be satisfied. Since "inequalty" is defined elsewhere as "a statement about the relative size or order of two objects", inequations are thingies like  x <= a, or  x < a, depending.  
A. Bossavit, 16 2 06
:Do you have a source? Melchoir 00:00, 17 February 2006 (UTC)
replies: text: I can see that "4=2+2" is a statement, but I don't see it as a problem to be solved.  Only some equations/inequations/inequalities fall into the category of "problems to be solved", while they ALL fall into the category of statements.  The distinction between an inequality and an inequation is well established on Wikipedia in several places.  Check the Table of mathematical symbols for one such example.  capitalist 03:28, 18 February 2006 (UTC)
replies: text: Agreed, but the reverse is not true; x=/=y does not imply x < y, so every inequation is not an inequality.  The article makes the same distintion between the two.  EDIT:  Actually though, as the article already points out, x=/=y implies either x>y or x<y (in a linearly ordered set), so in this case an inequation would always be an inequality as well.  But in the more general case, isn't it true that an inequation is a statement that the two expressions are not necessarily equal, but could be equal?  At any rate, there certainly is a useful distinction to be made between the two terms, which is my main point. capitalist 03:33, 23 February 2006 (UTC)
thread_title: Lead sentence

message: This article seems to say, that 'A neq B' means that A is definitely different from B. It is univerally true, that 'A neq B' - two unknown numbers are generally not the same, although they could be. Or 'A+B neq A*B' means 'addition and multiplcation is not the same', although a soultion to such eqation exist. Why not say: 'not equal' means that the truth of such statement can not be derived from existing axioms and laws.Medico80 (talk) 11:54, 30 March 2011 (UTC)
thread_title: Not the same, in general

message: The previous revision:
https://en.wikipedia.org/w/index.php?title=Inequation&oldid=467324239
made much more sense with respect to 'Not equal':
https://en.wikipedia.org/wiki/Not_equal
--JamesHaigh (talk) 21:42, 17 March 2012 (UTC)
replies: text: I've redirected Not equal to Inequality (mathematics), which, I think it is the right target.  --Lambiam 19:24, 18 March 2012 (UTC)
thread_title:  'Not equal' 

message: Epäyhtälö in English is not inequality, but inequation. Fixed.
Edit: sry, forgot the signature. 188.238.47.255 (talk) 11:03, 29 February 2016 (UTC)
thread_title:  Inequation in Finnish 

message: The article claims:
Sorry, not true.
The two statements in the third line follow from the first line but they do not express the same statement as the first line, so it's improper to say that the first line is shorthand for the third line. In particular the first line comments on the relationship between b and 1, but the third line is silent on that relationship.
And the conclusion of the sentence:
is false. That statement follows from the first line in the quoted material but not from the third line.
I can fix it but I'm not entirely sure what point is intended to be made.
One possibility:
Without  objection, I'll make the change.--S Philbrick(Talk) 20:28, 25 July 2020 (UTC)
replies: text: Ooooops! I just recognized that it was me who introduced this nonsense into the article. I have no idea what had come over me at that time. (I might have devoted too much attention to the neq-chain text and failed to notice that the leq-chain has 3 rather than 2 conjuncts.) - I completely agee with your suggested change. Thanks for noticing!. - Jochen Burghardt (talk) 13:54, 26 July 2020 (UTC)
replies: text:  I applied your edit, but sharpened the consequence. It might be wise if you cross-check it. - Jochen Burghardt (talk) 18:18, 1 August 2020 (UTC)
thread_title:  Potential edit 

message: Does anybody have a well-sourced idea where the name "inequation" (and similarly, "inequality") historically originated from? Triggered by my recent edit in the lead, "that an inequality <S>or a non-equality</S> holds" and its justification, I asked myself, why is e.g. the (reflexive) ordering "≤" called an inequality, but the (strict) partial ordering "is a proper divisor of" is not? I'm afraid this is a possible source of confusion for people just learning this stuff and knowing the prefix "in-" to denote negation.
The explanation I came up with is as follows:
<BLOCKQUOTE>
The names "inequation" (and "inequality") are much older than the modern notion of a relation. In these ancient days, few instances of what we today call a relation were known, viz. =, ≠, <, >, ≤, ≥, but nothing else. Since "=" was called "equality", all remaining relations were called "inequalities" (meaning, in today's words, "a relation, but not the equality relation" — this would explain why the negational prefix "in-" was used). In particular, in these ancient days, "is a proper divisor of" was not yet recognized as something of a similar kind as =, ≠, <, >, ≤, ≥, i.e. as a relation.
</BLOCKQUOTE>
If anybody can provide a supporting citation, I suggest that an explanation like the above one should be added (as a section "History") to the article. If someone knows a better explanation, I'd like to read about it. - Jochen Burghardt (talk) 12:40, 22 November 2021 (UTC)
thread_title:  History and naming 

message: Redirect for "not-equal sign" is needed. Kdammers (talk) 20:38, 14 April 2023 (UTC)
replies: text: The redirect Not-equal sign exists since 27 Sep 2018, and Not equals sign exists since 11 May 2008. I didn't check other spelling variants. - Jochen Burghardt (talk) 15:08, 15 April 2023 (UTC)
replies: text: I guess there was glitch in the network when I looked for it. Kdammers (talk) 20:15, 2 May 2023 (UTC)
thread_title:  redirect needed