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This article contains a translation of Équation from fr.wikipedia. |
I think that merging these two articles would be beneficial for those who are looking for basic descriptive information on actualy doing these mathematics. I do also think that the 'left hand/right hand' article could be maintained as succinct stand-alone resource for those searching specifiaclly for it. --anon
I vote against but I don't feel very strongly about it. I found my way here by searching Google for "right hand side". (I am writing a paper and I was curious if it is hypenated or not.) Jason Quinn 02:57, 5 June 2006 (UTC)
I vote against. I think that it would be enough to put reciprocal links for these two articles. Dmitry, 9 June 2006.
LIKE EQUATIOS ALGEBRAIC —Preceding unsigned comment added by 76.114.160.129 ( talk) 00:14, 23 April 2009 (UTC)
Aren't three horizontal bars often used to distinguish an identiy from an equation? Is this worth mentioning given the discussion of telling the difference between the two?
Solution point Directs here, but the article never mentions what a solution point is. I think that it should be mentioned, or the redirect should be removed. Unfortunately, I don't know what a solution point is, so I'm not sure if its notable enough or how much it relates to this article. Anyone have any ideas? cøøki ə Ξ (talk) 23:16, 30 August 2006 (UTC)
I look it up on google and couldn't find anything —Preceding unsigned comment added by 208.100.241.12 ( talk) 02:30, 13 June 2010 (UTC)
([Signed: Birdymckee, 24.8.2011])
([Signed: Birdymckee, 24.8.2011]) — Preceding unsigned comment added by Birdymckee ( talk • contribs) 22:58, 24 August 2011 (UTC)
Maybe also look here: Gowers: What is `solved' when one solves an equation? Boris Tsirelson 09:49, 12 March 2007 (UTC)
Currently, definitions of both functional equation and differential equation refer to this article. While I understand that many people have only seen algebraic equations, it would nevertheless be useful to explain that they are not the only type of equations considered in mathematics. Arcfrk 15:56, 19 March 2007 (UTC)
4/3+m/2 —Preceding unsigned comment added by 204.56.135.2 ( talk) 15:48, 10 October 2007 (UTC)
I don't dispute that Robert Recorde came up with the equals sign and therefore the first equation as we know it, but are you sure that what is in the top box is equivalent to what is in the bottom box in the picture? I have a source (Mathematics: From the Birth of Numbers by Jan Gullberg, page 107) that says that this equation in today's notation would be 14x+15=71, whereas the picture shows it to have the square root of x and absolute values of 15 and 71 (although the absolute values are the same when the numbers are positive). Just wondering what the source of this difference is, as it would not be the first error in Gullbergs' book.-- Terets ( talk) 14:02, 7 December 2008 (UTC)
I do not agree that an identity is an equation. In fact, this is an equality of functions. Therefore, the section "Identities" is misplaced here, and should be moved to Equality (mathematics). I have just edited the lead of this article to mention "identities" in it. D.Lazard ( talk) 10:40, 17 April 2013 (UTC)
are I am sure that that animated gif (or whatever it is) contains a lot of good information. However, to just let it loop and loop is distracting. It is like the adds on my cell phone; meant to distract you and aggravate you just enough to click on them. That image looks like it could be a very good interactive figure or exercise. There could be some great mathematical pedagogy there and a lot of people could learn from it. However, in its current form (a looping animated gif) I am sure that it is just annoying a large proportion of the people who find themselves trying to use this page. — Preceding unsigned comment added by 64.139.247.12 ( talk) 17:10, 7 June 2013 (UTC)
syed zain ul abdeen — Preceding unsigned comment added by Syedzainulabdeen ( talk • contribs) 11:01, 7 November 2014 (UTC)
I reverted three edits by Zedshort in the lead section. Here are my reasons in more detail.
(1)
I deleted the following text (and restored an earlier sentence):
"There are two kinds of equations: identity equations and conditional equations. An identity equation is true for all values of the variable. An conditional equation is true for only particular values of the variables"
The initial 3 sentences of the lead establish the terminology that an equation is something to be solved, i.e. (usually) not true for all values of the variables, but often only for a few (called the solutions). The deleted text is inconsistent with that; what it calls an "identity equation" is called an "identity", or an "identity equality" in the article. The text would fit perfectly into the equality article, after changing "equation" to "equality". Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
I suggest to stick with that terminology, even if some references use another one. All references should agree that it makes sense to distinguish between
I suggest that the wikipedia terminology is kept, and deviating terminology is mentioned. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
(2)
I deleted the following text:
An equation is analogous to a scale into which weights are placed. When equal weights of something (grain for example) are place into the two pans, the two weights cause the scale to be in balance and are said to be equal. If a quantity of grain is removed from one pan of the balance, an equal amount of grain must be removed from the other pan to keep the scale in balance. Likewise, to keep an equation in balance, the same operations of addition, subtraction, multiplication and division must be performed on both sides of an equation for it to remain an equality.
My reason was the same as above: the scale analogy fits well with "equality", but doesn't fit with "equation". It could be adapted to fit with the latter by asking something like "how many grains have to be put on the left scale to obtain balance if ...?", i.e. by giving a Word problem (mathematics education) that amounts to solving an equation. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
When an equation is solved, it is important to keep track of the solution set, while the deleted text suggests that "balance" should be kept. I repeat my counterexample from my edit summary: squaring an equation usually changes the solution set (and therefor has to be handled with care), but doesn't change "balance" (whatever that word means in absense of particular values for the variables). Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
(3)
I deleted the following text:
Each side of an equation is called a member of the equation. Each member will contain one or more terms. The equation, has two members: and . The left member has three terms and the right member one term. The variables are x and y and the parameters are A, B, and C.
It introduces unusual (to say the least) terminology; I suggest to change "members" to "left-hand side and right-hand side", which is more common. I know of two meanings of "term", explained at term (logic) and Addition#Notation and terminology, but none of them makes sense in the deleted sentence "Each member will contain one or more terms". If the former notion is meant, it should be "Both the lhs and the rhs is a term"; if the latter notion is meant, it should be "Many, but not all, equations contain one or more terms on their lhs and rhs". Finally it suggests that the distinction between vairables and parameters (a notion that wasn't even mentioned before) is obvious, probably from the naming. On the contrary, I think that the equation can be solved wrt. an arbitrary nonempty subset of {x,y,A,B,C}, thus giving rise to 31 mathematical tasks, some of which are more, and some less common. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
More general, while it may be a good idea to have an example already in the lead, I think it should be kept simple (and understandable to a wide audience). So I'd prefer to use the historical equation "14x+15=71" from the picture, for which the solution x=4 is easily understood. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
BTW @ Zedshort: you should take notice of the WP:BRD policy, although I won't insist on it here. - Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
My main issue is that the distinction I sketched above in (1), Nr.1.-3. should not be blurred. So, ignoring naming issues for the moment, can we agree that distinction makes sense?
If yes, I'd suggest to agree next on a name for each of them, to be used as "main name" in wikipedia articles, while deviating names are to be mentioned in side remarks. Moreover, I think we'd need a name for the general concept that is common to Nr.1.-3; I'll call it "Nr.0." for brevity in the following discussion.
My suggestions for Nr.1., 2., and 3. are "identity equality", "conditional equality", and "equation", respectively (as I already wrote in (1)), and to use "equality" for Nr.0.
@ Zedshort: It seems that your 1st source Kells.1964 agrees with my naming suggestion for 1. and 2., but prefers "equation" for 0.; your 2nd source Brooks.1996 also uses "identity" for 1. and "equality" for (I think) 0.; your 3rd source Richardson.1966 uses "identical equation" or "identity" for 1., "conditional equation" for (I think) 2., and again "equation" for 0. From this, I guess your point is to use "equation" for 0., while you may agree with me on Nr.1.-3. - did I get that right?
In this case (provided there is consensus about the above distinction), we'd need to distinguish 3. from 0. by their use (3.="equation as problem task", 0.="just an equation, with no particular use given", 1.="asserted equation, or identity equation"). My point is that this would complicate the article text (we'd need to replace "equation" by "equation to be solved", and then "equality" by "equation"), and would even require renaming of the article (as it is about Nr.3, i.e. solving, except for a brief subsection "Identities" and your recent lead insertions). Ease of presentation is the main reason why I like(d) the terminology of the article (as suggested above for keeping).
To complicate things, we need to delimitate in any case from other articles, viz. equality (mathematics) (a mess) and identity (mathematics) (giving undue emphasis to trigonometrical and exponential laws) about Nr.1., and theory of equations (should better be integrated here as a history section) about Nr.3.
I split off some minor points below into subsubsection, signing each one separately, and hoping that this makes it easier to reply in an appropriate place. - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
All sources given so far agree in using "equation" for the general concept (meaning "Nr.0" above, i.e. two expressions joined by "=").
(I found three more references from the fields of automated theorem proving and theoretical computer science with the same usage (Caution: Jargon):
)
Thus I meanwhile think
Zedshort was right (apologies!).
As a consequence, I suggest:
- Jochen Burghardt ( talk) 16:41, 22 August 2016 (UTC)
Today, I started editing a new suggestion for the article at User:Jochen Burghardt/sandbox2. Up to now, I only changed the lead, using stuff from de:Gleichung and simple:Equation which both support the above suggestions (while the quality article fr:Équation seems to be restricted to equation solving), and incorporating some sources from this talk page. Comments (best placed on this talk page in a new section, I suppose) and constructive edits in the sandbox are welcome. - Jochen Burghardt ( talk) 11:19, 13 September 2016 (UTC)
As for the balance analogy: I'm not against it, but it needs to be phrased carefully in order not to be misleading. I think it is most useful for notion Nr.1 and 2., but dangerous for Nr.3., as my above squaring example should illustrate (another one is multiplying both sides with zero; this no doubt keeps the balance, but widens the solution set to all numbers). Moreover, the analogy is given (and depicted) in an own section "Analogous illustration" (which should be cleaned up, too, in this respect). - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
@ Zedshort: your notion of "term" (sourced from Richardson.1966) appears to agree with that of Addition#Notation and terminology. However, there are certainly equations that don't have a sum on either side, so your sentence "Each member will contain one or more terms", while fitting on your particular example, doesn't hold for all equations, as already Wcherowi (thanks!) pointed out. - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
As for as a second example in the lead: I'd feel it would make the lead too long, and would better fit into section "Polynomial equations". Maybe, if we can illustrate another important point on this example, it's worth to be in the lead, nevertheless. Maybe, we can combine it with the lead paragraph starting "In geometry, ...", giving e.g. the parametric equation of a circle (, to be moved up from section "Parameters and unknowns" in this case)? This whould have 2 variables and a parameter, too, and in addition a geometric meaning. - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
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I recently grouped the essentially-identical classes of differential equation, integral equation and integro-differential equation together. The change was reverted as "not an improvement". I think that showing the connection between these nominally different types of equations is indeed an improvement, even if my particular wording was not perfect. I have made my changes again. If anyone wants to revert them, please explain here why that is done. LachlanA ( talk) 13:57, 28 May 2019 (UTC)
At: Equation#Types of equations, should the list begin with something like: "constant equation for degree zero", since equations like "y+2=5" are typically the first type of equations that students solve? (And to be more in sync with this article: Degree of a polynomial#Names of polynomials by_degree) DKEdwards ( talk) 06:45, 23 January 2022 (UTC)
This
level-3 vital article is rated C-class on Wikipedia's
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This article contains a translation of Équation from fr.wikipedia. |
I think that merging these two articles would be beneficial for those who are looking for basic descriptive information on actualy doing these mathematics. I do also think that the 'left hand/right hand' article could be maintained as succinct stand-alone resource for those searching specifiaclly for it. --anon
I vote against but I don't feel very strongly about it. I found my way here by searching Google for "right hand side". (I am writing a paper and I was curious if it is hypenated or not.) Jason Quinn 02:57, 5 June 2006 (UTC)
I vote against. I think that it would be enough to put reciprocal links for these two articles. Dmitry, 9 June 2006.
LIKE EQUATIOS ALGEBRAIC —Preceding unsigned comment added by 76.114.160.129 ( talk) 00:14, 23 April 2009 (UTC)
Aren't three horizontal bars often used to distinguish an identiy from an equation? Is this worth mentioning given the discussion of telling the difference between the two?
Solution point Directs here, but the article never mentions what a solution point is. I think that it should be mentioned, or the redirect should be removed. Unfortunately, I don't know what a solution point is, so I'm not sure if its notable enough or how much it relates to this article. Anyone have any ideas? cøøki ə Ξ (talk) 23:16, 30 August 2006 (UTC)
I look it up on google and couldn't find anything —Preceding unsigned comment added by 208.100.241.12 ( talk) 02:30, 13 June 2010 (UTC)
([Signed: Birdymckee, 24.8.2011])
([Signed: Birdymckee, 24.8.2011]) — Preceding unsigned comment added by Birdymckee ( talk • contribs) 22:58, 24 August 2011 (UTC)
Maybe also look here: Gowers: What is `solved' when one solves an equation? Boris Tsirelson 09:49, 12 March 2007 (UTC)
Currently, definitions of both functional equation and differential equation refer to this article. While I understand that many people have only seen algebraic equations, it would nevertheless be useful to explain that they are not the only type of equations considered in mathematics. Arcfrk 15:56, 19 March 2007 (UTC)
4/3+m/2 —Preceding unsigned comment added by 204.56.135.2 ( talk) 15:48, 10 October 2007 (UTC)
I don't dispute that Robert Recorde came up with the equals sign and therefore the first equation as we know it, but are you sure that what is in the top box is equivalent to what is in the bottom box in the picture? I have a source (Mathematics: From the Birth of Numbers by Jan Gullberg, page 107) that says that this equation in today's notation would be 14x+15=71, whereas the picture shows it to have the square root of x and absolute values of 15 and 71 (although the absolute values are the same when the numbers are positive). Just wondering what the source of this difference is, as it would not be the first error in Gullbergs' book.-- Terets ( talk) 14:02, 7 December 2008 (UTC)
I do not agree that an identity is an equation. In fact, this is an equality of functions. Therefore, the section "Identities" is misplaced here, and should be moved to Equality (mathematics). I have just edited the lead of this article to mention "identities" in it. D.Lazard ( talk) 10:40, 17 April 2013 (UTC)
are I am sure that that animated gif (or whatever it is) contains a lot of good information. However, to just let it loop and loop is distracting. It is like the adds on my cell phone; meant to distract you and aggravate you just enough to click on them. That image looks like it could be a very good interactive figure or exercise. There could be some great mathematical pedagogy there and a lot of people could learn from it. However, in its current form (a looping animated gif) I am sure that it is just annoying a large proportion of the people who find themselves trying to use this page. — Preceding unsigned comment added by 64.139.247.12 ( talk) 17:10, 7 June 2013 (UTC)
syed zain ul abdeen — Preceding unsigned comment added by Syedzainulabdeen ( talk • contribs) 11:01, 7 November 2014 (UTC)
I reverted three edits by Zedshort in the lead section. Here are my reasons in more detail.
(1)
I deleted the following text (and restored an earlier sentence):
"There are two kinds of equations: identity equations and conditional equations. An identity equation is true for all values of the variable. An conditional equation is true for only particular values of the variables"
The initial 3 sentences of the lead establish the terminology that an equation is something to be solved, i.e. (usually) not true for all values of the variables, but often only for a few (called the solutions). The deleted text is inconsistent with that; what it calls an "identity equation" is called an "identity", or an "identity equality" in the article. The text would fit perfectly into the equality article, after changing "equation" to "equality". Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
I suggest to stick with that terminology, even if some references use another one. All references should agree that it makes sense to distinguish between
I suggest that the wikipedia terminology is kept, and deviating terminology is mentioned. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
(2)
I deleted the following text:
An equation is analogous to a scale into which weights are placed. When equal weights of something (grain for example) are place into the two pans, the two weights cause the scale to be in balance and are said to be equal. If a quantity of grain is removed from one pan of the balance, an equal amount of grain must be removed from the other pan to keep the scale in balance. Likewise, to keep an equation in balance, the same operations of addition, subtraction, multiplication and division must be performed on both sides of an equation for it to remain an equality.
My reason was the same as above: the scale analogy fits well with "equality", but doesn't fit with "equation". It could be adapted to fit with the latter by asking something like "how many grains have to be put on the left scale to obtain balance if ...?", i.e. by giving a Word problem (mathematics education) that amounts to solving an equation. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
When an equation is solved, it is important to keep track of the solution set, while the deleted text suggests that "balance" should be kept. I repeat my counterexample from my edit summary: squaring an equation usually changes the solution set (and therefor has to be handled with care), but doesn't change "balance" (whatever that word means in absense of particular values for the variables). Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
(3)
I deleted the following text:
Each side of an equation is called a member of the equation. Each member will contain one or more terms. The equation, has two members: and . The left member has three terms and the right member one term. The variables are x and y and the parameters are A, B, and C.
It introduces unusual (to say the least) terminology; I suggest to change "members" to "left-hand side and right-hand side", which is more common. I know of two meanings of "term", explained at term (logic) and Addition#Notation and terminology, but none of them makes sense in the deleted sentence "Each member will contain one or more terms". If the former notion is meant, it should be "Both the lhs and the rhs is a term"; if the latter notion is meant, it should be "Many, but not all, equations contain one or more terms on their lhs and rhs". Finally it suggests that the distinction between vairables and parameters (a notion that wasn't even mentioned before) is obvious, probably from the naming. On the contrary, I think that the equation can be solved wrt. an arbitrary nonempty subset of {x,y,A,B,C}, thus giving rise to 31 mathematical tasks, some of which are more, and some less common. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
More general, while it may be a good idea to have an example already in the lead, I think it should be kept simple (and understandable to a wide audience). So I'd prefer to use the historical equation "14x+15=71" from the picture, for which the solution x=4 is easily understood. Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
BTW @ Zedshort: you should take notice of the WP:BRD policy, although I won't insist on it here. - Jochen Burghardt ( talk) 17:27, 4 August 2016 (UTC)
My main issue is that the distinction I sketched above in (1), Nr.1.-3. should not be blurred. So, ignoring naming issues for the moment, can we agree that distinction makes sense?
If yes, I'd suggest to agree next on a name for each of them, to be used as "main name" in wikipedia articles, while deviating names are to be mentioned in side remarks. Moreover, I think we'd need a name for the general concept that is common to Nr.1.-3; I'll call it "Nr.0." for brevity in the following discussion.
My suggestions for Nr.1., 2., and 3. are "identity equality", "conditional equality", and "equation", respectively (as I already wrote in (1)), and to use "equality" for Nr.0.
@ Zedshort: It seems that your 1st source Kells.1964 agrees with my naming suggestion for 1. and 2., but prefers "equation" for 0.; your 2nd source Brooks.1996 also uses "identity" for 1. and "equality" for (I think) 0.; your 3rd source Richardson.1966 uses "identical equation" or "identity" for 1., "conditional equation" for (I think) 2., and again "equation" for 0. From this, I guess your point is to use "equation" for 0., while you may agree with me on Nr.1.-3. - did I get that right?
In this case (provided there is consensus about the above distinction), we'd need to distinguish 3. from 0. by their use (3.="equation as problem task", 0.="just an equation, with no particular use given", 1.="asserted equation, or identity equation"). My point is that this would complicate the article text (we'd need to replace "equation" by "equation to be solved", and then "equality" by "equation"), and would even require renaming of the article (as it is about Nr.3, i.e. solving, except for a brief subsection "Identities" and your recent lead insertions). Ease of presentation is the main reason why I like(d) the terminology of the article (as suggested above for keeping).
To complicate things, we need to delimitate in any case from other articles, viz. equality (mathematics) (a mess) and identity (mathematics) (giving undue emphasis to trigonometrical and exponential laws) about Nr.1., and theory of equations (should better be integrated here as a history section) about Nr.3.
I split off some minor points below into subsubsection, signing each one separately, and hoping that this makes it easier to reply in an appropriate place. - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
All sources given so far agree in using "equation" for the general concept (meaning "Nr.0" above, i.e. two expressions joined by "=").
(I found three more references from the fields of automated theorem proving and theoretical computer science with the same usage (Caution: Jargon):
)
Thus I meanwhile think
Zedshort was right (apologies!).
As a consequence, I suggest:
- Jochen Burghardt ( talk) 16:41, 22 August 2016 (UTC)
Today, I started editing a new suggestion for the article at User:Jochen Burghardt/sandbox2. Up to now, I only changed the lead, using stuff from de:Gleichung and simple:Equation which both support the above suggestions (while the quality article fr:Équation seems to be restricted to equation solving), and incorporating some sources from this talk page. Comments (best placed on this talk page in a new section, I suppose) and constructive edits in the sandbox are welcome. - Jochen Burghardt ( talk) 11:19, 13 September 2016 (UTC)
As for the balance analogy: I'm not against it, but it needs to be phrased carefully in order not to be misleading. I think it is most useful for notion Nr.1 and 2., but dangerous for Nr.3., as my above squaring example should illustrate (another one is multiplying both sides with zero; this no doubt keeps the balance, but widens the solution set to all numbers). Moreover, the analogy is given (and depicted) in an own section "Analogous illustration" (which should be cleaned up, too, in this respect). - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
@ Zedshort: your notion of "term" (sourced from Richardson.1966) appears to agree with that of Addition#Notation and terminology. However, there are certainly equations that don't have a sum on either side, so your sentence "Each member will contain one or more terms", while fitting on your particular example, doesn't hold for all equations, as already Wcherowi (thanks!) pointed out. - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
As for as a second example in the lead: I'd feel it would make the lead too long, and would better fit into section "Polynomial equations". Maybe, if we can illustrate another important point on this example, it's worth to be in the lead, nevertheless. Maybe, we can combine it with the lead paragraph starting "In geometry, ...", giving e.g. the parametric equation of a circle (, to be moved up from section "Parameters and unknowns" in this case)? This whould have 2 variables and a parameter, too, and in addition a geometric meaning. - Jochen Burghardt ( talk) 10:48, 5 August 2016 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Equation. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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(last update: 18 January 2022).
Cheers.— InternetArchiveBot ( Report bug) 14:52, 2 August 2017 (UTC)
I recently grouped the essentially-identical classes of differential equation, integral equation and integro-differential equation together. The change was reverted as "not an improvement". I think that showing the connection between these nominally different types of equations is indeed an improvement, even if my particular wording was not perfect. I have made my changes again. If anyone wants to revert them, please explain here why that is done. LachlanA ( talk) 13:57, 28 May 2019 (UTC)
At: Equation#Types of equations, should the list begin with something like: "constant equation for degree zero", since equations like "y+2=5" are typically the first type of equations that students solve? (And to be more in sync with this article: Degree of a polynomial#Names of polynomials by_degree) DKEdwards ( talk) 06:45, 23 January 2022 (UTC)