Talk:Inequation

Lead sentence

"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)

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)

An inequality is an inequation. "Problem to be solved" seems like a point of view. For example, someone could claim that i = sqrt(-1) is a problem to be solved, while for many there's no problem to be solved there. Since 1 < 2, then it's true that 2 =/= 3. So every inequality is an inequation, in an ordered field.

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)

Not the same, in general

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)

'Not equal'

The previous revision:

https://en.wikipedia.org/enwiki/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)

I've redirected Not equal to Inequality (mathematics), which, I think it is the right target.  --Lambiam 19:24, 18 March 2012 (UTC)

Merger proposal

This subject is not substantively different from the topic of inequality (mathematics). -99.121.57.103 (talk) 08:02, 24 May 2012 (UTC)

Concerning the discussion about the lead sentence above, I suggest to stick with the setting from the equation article:

"In mathematics an equation is an expression of the shape A = B, where A and B are expressions containing one or several variables called unknowns. An equation looks like an equality, but has a very different meaning: An equality is a mathematical statement that asserts that the left-hand side and the right-hand side of the equals sign (=) are the same or represent the same mathematical object; for example 2 + 2 = 4; is an equality. On the other hand, an equation is not a statement, but a problem consisting in finding the values, called solutions, that, when substituted to the unknowns, transform the equation into an equality. For example, 2 is the unique solution of the equation x + 2 = 4, in which the unknown is x."

and, in the same sense, the Equality_(mathematics) article:

"One must not confuse equality and equation, although they are written similarly. An equality is an assertion, while an equation is the problem of finding values of some variables, called unknowns, to get an equality. Equation may also refer to an equality relation that is satisfied only for the values of the variables that one is interested on. For example x² + y² = 1 is the equation of the unit circle."

Strictly mathematically speaking, we should distinguish between a proposition that is assumed and a proposition that is to be proven; moreover, we shouldn't ignore quantifiers, at least in internal discussions on this talk page. Using these notions, an equation is commonly understood as a proposition of the form $\exists x_{1},...,x_{n}:s=t$, where $s$ and $t$ denote expressions in which the variables $x_{1},...,x_{n}$ may occur. To (constructively) prove such an equation means to find solutions for $x_{1},...,x_{n}$. On the other hand, an equality is understood as a proposition of the form $\forall x_{1},...,x_{n}:s=t$. This is what the quote equation article explains in simple words. Commonly, equalities like $\forall x,y:x+y=y+x$ are assumed as axioms, and an equation like $\exists x:x+2=4$ is to be proven/solved. Things are similar for inequations, except that $=$ is replaced by $\neq$, $\leq$, or $<$, or ...

Corncerning the merger proposal, I suggest to keep both articles separated, parallel to the structure of the equality/equation articles, and for the same reason (tried to explain above). Jochen Burghardt (talk) 13:47, 9 June 2013 (UTC)