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"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
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.
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)
The previous revision:
https://en.wikipedia.org/?title=Inequation&oldid=467324239
made much more sense with respect to 'Not equal':
-- JamesHaigh ( talk) 21:42, 17 March 2012 (UTC)
This subject is not substantively different from the topic of inequality (mathematics). - 99.121.57.103 ( talk) 08:02, 24 May 2012 (UTC)
and, in the same sense, the Equality_(mathematics) 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."
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, [1] at least in internal discussions on this talk page. Using these notions, an equation is commonly understood as a proposition of the form , where and denote expressions in which the variables may occur. To (constructively) prove such an equation means to find solutions for . On the other hand, an equality is understood as a proposition of the form . [2] This is what the quote equation article explains in simple words. Commonly, equalities like are assumed as axioms, and an equation like is to be proven/solved. Things are similar for inequations, except that is replaced by , , or , or ..."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."
Inequations exist in modulo arithmetic, but inequalities do not. 131.215.220.163 ( talk) 23:25, 1 July 2014 (UTC)
Counter
Although the statements are true, an inequality is a comparison between two numbers (ex. 1≤6) while an equation is two numbers and it's answer (ex. 1+6=7). The two subjects are not alike. 204.210.154.199 ( talk) 19:07, 4 January 2015 (UTC)
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)
The article claims:
:
is shorthand for
- ,
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:
which implies that also .
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:
:
is shorthand for
which also implies that .
Without objection, I'll make the change.-- S Philbrick (Talk) 20:28, 25 July 2020 (UTC)
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 or a non-equality 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:
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.
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)
Redirect for "not-equal sign" is needed. Kdammers ( talk) 20:38, 14 April 2023 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
"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
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.
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)
The previous revision:
https://en.wikipedia.org/?title=Inequation&oldid=467324239
made much more sense with respect to 'Not equal':
-- JamesHaigh ( talk) 21:42, 17 March 2012 (UTC)
This subject is not substantively different from the topic of inequality (mathematics). - 99.121.57.103 ( talk) 08:02, 24 May 2012 (UTC)
and, in the same sense, the Equality_(mathematics) 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."
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, [1] at least in internal discussions on this talk page. Using these notions, an equation is commonly understood as a proposition of the form , where and denote expressions in which the variables may occur. To (constructively) prove such an equation means to find solutions for . On the other hand, an equality is understood as a proposition of the form . [2] This is what the quote equation article explains in simple words. Commonly, equalities like are assumed as axioms, and an equation like is to be proven/solved. Things are similar for inequations, except that is replaced by , , or , or ..."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."
Inequations exist in modulo arithmetic, but inequalities do not. 131.215.220.163 ( talk) 23:25, 1 July 2014 (UTC)
Counter
Although the statements are true, an inequality is a comparison between two numbers (ex. 1≤6) while an equation is two numbers and it's answer (ex. 1+6=7). The two subjects are not alike. 204.210.154.199 ( talk) 19:07, 4 January 2015 (UTC)
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)
The article claims:
:
is shorthand for
- ,
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:
which implies that also .
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:
:
is shorthand for
which also implies that .
Without objection, I'll make the change.-- S Philbrick (Talk) 20:28, 25 July 2020 (UTC)
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 or a non-equality 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:
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.
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)
Redirect for "not-equal sign" is needed. Kdammers ( talk) 20:38, 14 April 2023 (UTC)