Talk:Elementary algebra/Archive 1

To do list

1] Order of Operations

2] Settle problem(s) with 'Laws'/Axioms section

3] Basic Section on Inequalities

4] Address the special properties of 0

EulerGamma 23:34, 6 September 2006 (UTC)

Topics

<<Comment -- breaking the topics down as follows may not be such a good idea. While it might be useful for a public school teacher who has to teach the concepts to students, it might not be the best for this which is just supposed to describe what algebra is -- besides Pascal's Triangle is not specifically a topic from algebra. -- Paul Hsieh>>

Yes, it wasn't really very well thought out. I moved it to Elementary algebra just to get rid of it, since I didn't want to upset its author by deleting it. It can probably be deleted now, but I'll leave it on the talk page for the moment. --Zundark, 2001 Oct 10

Expansion of Two Brackets

Difference of Two Squares

Squares

Important Expansions

Factoring Quadratic Expressions

Simple Factoring

Harder Factoring

---

'Laws' of elementary algebra

According to [1], some of the axioms/laws(?) stated in the Laws section of the article are actually axioms of fields.

We need a section on order of operations. Order of operations was not a part of basic arithmetic.--BlackGriffen

---

An equation is any statement that claims that two expressions are equal. These expressions can naturally contain variables, numbers, absolute values or anything else. An identity is an equation that's claimed to be true for all possible values of the variable, such as "x+y=y+x". An inequality is not an equation; it involves ≤ or <, not =. (But algebra talks about inequalities, so they should be mentioned.) AxelBoldt 00:50 Oct 14, 2002 (UTC)

Any statement that two quantities are equal is an equation, but even then there is no "claim," merely a statement, and the statement is not that they are "the same" (which is what you put in and I took out) but that they are equal in numerical value. But an equation is a statement that "equates" two expressions, and the relationship may not be equality -- or would you have it that "x is less than or equal to 5" is not an equation? What I likened to a verb in the definition is still "is" which is what makes it an equation: (x) = (≤ 5). [I hope that's what I meant to say, but my browser shows all the symbols (including the one after "it involves" in your posting) as rectangles -- the symbol before the "5" should be "less than or equal to."] So equality is not the only relationship that can be expressed by an equation, before you get to the fact that a "let" statement is also an equation, as in: "Let x be a positive integer less than 5," where the expression on the right of the "=" is the set of integers (1,2,3,4), which are the solutions of that equation. So every statement of equality is an equation, but not every equation is a statement of equality: Some are statements of equivalency, and a cup of coffee may be equivalent to a dollar bill in value, but they are not "the same" or even equal. -- isis 04:00 Oct 14, 2002 (UTC)

---

Is there specifically a requirement that abstract algebra must be taught only to college seniors? I took trigonometry/pre-calculus in 8th grade (and got a C+, but... ya know)... yet it is impossible for me to take abstract algebra when I'm a junior in college?

Oh, and I have another question. Is there a property that would allow me (in a proof) to say that, if x² = y², then x = y?

When x = a and y = -a, you will find that x² = y² is true, but that x = y is false. Which tends to suggest that there is no such property. -- Derek Ross

Well, no, because it can be trivially disproved. Given x = 2 and y = -2, x² = y² = 4, but 2 != -2 orthogonal 21:57, 19 Nov 2003 (UTC)

Of course, this is true if x and y are non-negative. Paul August 19:42, Jul 24, 2004 (UTC)

Divide by zero

Silly question; should divide by zero be addressed on this page?--66.44.108.150 14:28, 5 Aug 2004 (UTC) I believe we should talk about zero division in this section

Absolutely, we should... starting with the definition of devision and explaining the adage that we may divide into zero but not by zero. B.Wind 07:37, 7 December 2005 (UTC)

If a = b then ac = bc for any c

The converse is true only if c is nonzero. Multiplying an algebraic equation by something that could be zero expands the solution set. B.Wind 07:37, 7 December 2005 (UTC)

I think you mean to bring up the rule "if ac = bc, then a=b" which is true, except in the case of zero, but the rule "If a = b then ac = bc for any c" is indeed a different rule that holds up for all real numbers, a, b, and c. I mean, if c=0, we simply have the trivial case (that is, the case that is true, but trivial, like 1=1, or in this case, 0=0). Right? Jehan60188 —Preceding unsigned comment added by Jehan60188 (talk • contribs) 20:19, 19 August 2008 (UTC)

Order of operations

I deleted the "order of operations" section because I didn't think it was tremendously clear and not everyone follows those rules as stated (in my experience at least). Usually the order of operations is clear from the typesetting -- I don't think mathematicians work with an "order of precedence" like computer compilers. It wasn't particularly clear what was meant by groupings anyway. I don't think it added much to the article. If anyone wanted to reinstate it or had strong feeligns I would not object. --Richard Clegg 13:20, 13 April 2006 (UTC)

missing law

In EA, any numbers are equal or not equal, for example : a = b or a =/ b. Lincher 20:29, 18 April 2006 (UTC)

a set is a collection of object or things. —Preceding unsigned comment added by 124.105.233.36 (talk) 10:35, 21 July 2008 (UTC)

Good Article Nomination

Judged against good article criterion I failed this but only just. It is good but I don't think quite "good article" yet.

1) It is well written: (fail) This article is well-written by the standards of mathematics articles but it does have some specific failings which I think should be addressed. The main failing (to my mind) is the list of elementary "laws", the axioms of elementary algebra. This is very clear except that it is a mixture of the axioms themselves and illustrative examples and subcases and these are distinguished only by indentation. For example: the expoentiation is commutative has three levels of indentation, the axiom, a corrollary of the axiom (I presume) and an example of this followed by another corrollary. This becomes confusing. In one case I am not really sure what the indentation indicates and the indentation may be an error. Perhaps the list should be subdivided into the properties of the operations, the properties of the = operator and the properties of > and <. Possibly reference equivalence relationships and partial orderings in set theory here?

2) It is factually accurate and verifiable: (marginal pass) I spotted no errors. However, the references section is very poor. I would expect to see a reference to at least one modern Algebra text that I could purchase in a shop. The online historical reference is nice but it's not actually very usable (page scans are slow even on broadband, no hyperlinks, in old-fashioned style). It would be good to see a reference to a modern text a high-school student could purchase to learn from.

3) Broad in coverage: (marginal fail) The list of "see also" seemed arbitrary to me -- not sure why number line or binomial are there but other things were left out. I suppose this could be said of any article. There was no sense of how this fundamental area connects to other areas of mathematics. It was (I think) assumed throughout that we were working with the reals but everything would work with complex numbers (except > and < would apply only to the argument). I would hope to see more about where this topic fits in.

4) It adheres to the neutral point of view policy: (pass).

5) It is stable: (pass)

6) It contains images to illustrate it, where possible: (marginal pass) It contains no images but I'm not sure what on earth WOULD illustrate something like this.

Sorry for failing -- it is on the way there but needs some few things doing to it. --Richard Clegg 19:56, 13 April 2006 (UTC)

I completely agree with you failing the article, and this is of great importance to remedy. Although I think that you were being a bit gentle with your critique:

1) If the article fails to express the difference between laws, axioms, corrollary, and so on, then how could it be "well written" by the standards of mathematics. To me, it did not seem too well written at all. Personally, I do not think the article has to be too math-focused, though, as it is more on algebra in the context of how it is first taught in schools.

4) To me, it had a lot of POV: "most basic form of algebra", "Advanced topic [...] taught to college seniors", and so on.

5) If by 'stable', you mean 'consistent', then I agree. I am not quite familiar with any grading policies for good articles and its terminology.

6) I can think of a few things: Number line (showing how a - b = a + (-b) or something like that), Weight scale [thingy] (showing how one can manipulate an equation by doing 'something' to both sides), and so on.

I will be working on this article for now because it seems very important. EulerGamma 22:44, 6 September 2006 (UTC)

Its great that you'll give this article a bit of attention, it and Algebra are important articles but severley lacking. The Wikipedia:Version 1.0 Editorial Team has Algebra as one of its 150 core topics pages, some of the most important pages. The good article criteria can be found at Wikipedia:What is a good article? it would be brilliant if we could bring this upto that standard. The number line seems important. Weight scales are perhaphs more a topic for a page on pedological methods in Category:Mathematics education. The trick with this article will be to make it encyclopedic as distinct to a textbook. --Salix alba (talk) 23:12, 6 September 2006 (UTC)

A "Set"

It is not even mentioned on the page though it is a very important concept for young children because they can associate it to sets they know. I think it should be defined in the text or at least pointed to in another WP page. Lincher 19:57, 18 April 2006 (UTC)

I am not quite sure if sets are included in elementary algebra, but I really do not remember to much from when I was taught. Are you sure this is talked about? EulerGamma 22:33, 6 September 2006 (UTC)

Indeed, while we did cover sets in school, it was typically taught in different leasons to the algebra leasons. Actually my fairly current GCSE maths (ages 14-16) text book does not mention sets at all, its true, standards are declining! There may be a need for a topics in school mathematics category or info box, where elementary algebra and sets could be covered. --Salix alba (talk) 22:47, 6 September 2006 (UTC)

Systems of equations: over/underdetermined systems

I added a little bit about systems of equations with no or infinitely many solutions. I tried to do it in a way suitable for non-mathematicians, but I thought it might be important. Firstly, the section provides some tricks to easily check whether a system is solvable before even trying to solve it (might be nice for large systems). Secondly, I hope interested people will wonder when and why a system is over- or underdetermined, click to read more math pages and get sucked in :)

Anyway, If it's too complicated, feel free to edit it or move it to another page. --CompuChip 16:11, 15 November 2006 (UTC)

I cleaned up that new section a little bit, I thought the equation types with equal signs one after another (having three equal signs or more in a single line, example: x + 2 - 2 = x + 0 = x ) were sort of confusing. I also added a rather obvious example of a system with no solutions. However, I did not quite understand the paragraph that started with 'Notice that the left hand side of the second equation is exactly...'. I didn't want to edit it, since I kind of saw where you were going, but as I did not fully understand it, I left it as it was. Maybe you could clarify a little bit.

I'm going to be adding a thing or two about equation systems later on, but as you said, feel free to edit it or move it if it gets too messy, as I am a rather new (registered) user and not really experienced with editing and so forth. (Quadrivium 16:27, 16 November 2006 (UTC))

Well, actually what I meant to say is, that the solvability of the system depends on whether or not the equations are linearly dependent (that is: the rows of the corresponding matrix are multiples) - but in such a way that most people would understand it. I'll try to clarify more. --CompuChip 19:47, 16 November 2006 (UTC)

Great. Definitely looking forward to it :) It's probably good if you don't add any matrixes (while still making your point)- in my opinion it's too deep for this. We're talking about elementary stuff here, right? Also, I don't know if I should create a separate issue here, but there is something that seems sort of messy. The System of linear equations article seems very different from the information in this article. It seems a bit too theoretical to me, since it provides no examples. In opposition, this article hardly defines what a system of linear equation is, while providing many examples. I was thinking, maybe we could merge all these examples we are creating with that article (which is referred to right below the title 'Example of over- and undetermined system') killing two birds with one stone. We would be adding examples to System of linear equations (which, correct me if I'm wrong, but seem to be needed in that article) and also, we would be cleaning up Elementary algebra which seems to be piling up with disorganized --and maybe too advanced-- knowledge. What do you think? (Quadrivium 20:16, 16 November 2006 (UTC))

Edit; Oh and by the way. I think that paragraph is clearer now. However, I can't help but predict this is going to get too big (and kind of disorganized too) for elementary algebra. I am no expert on mathematical fields, but if that section on itself gets bigger than the rest of the article, then I think we should probably make one big article about it (or merge it with the one that's already made, with all the theory and all), while making some basic references to it on Elementary algebra. I'm new here, so could anyone tell me how (or where) should I suggest this? Comments appreciated. (Quadrivium 21:01, 16 November 2006 (UTC))

Encyclopedia, not a tutor

Not that it is too much of a problem, but it seems to me that the article is too intent on tutoring the reader than explaining it as an encyclopedia. In my editing, I tried to take a lot of this out, but ended up keeping a little bit in the end. (I took out or replaced some things that appeared to baby the reader too much or used the terms 'we' or 'our'. And there were a LOT of instances of we)

I did a pretty good edit of the article (in my opinion), but someone needs to make my (lack of) wordchoice better. Also, I didnt even touch the 'laws', as that will take some serious editing and time. Hope I helped.

PS: arent most of those the axioms of (formal) arithmetic? (just expressed in elementary algebra?) EulerGamma 23:28, 6 September 2006 (UTC)

Merging Suggestion

I am proposing a merging of part of this article's info on Systems of Linear Equations with System of linear equations and Simultaneous equations. Comments are appreciated and the explanation and discussion are being held here: Wikipedia talk:WikiProject Mathematics. (Quadrivium 23:17, 17 November 2006 (UTC))

First sentence kind of insulting

As a first-year student in College Algebra at college, I feel kind of offended by the first line of this wiki article :(.

Quadratic equations

The use of "were" in the first sentence of this section is the subjunctive, which is correct. I've reverted to a previous version which included this rather than the word "was" since the latter is incorrect. Xantharius 16:46, 1 June 2007 (UTC)

if $3^{x}=10$ then $x=\log _{3}10.$

$2^{8}=256$

$\log _{2}256=77.06367888997918597471715704947$ ???

205.206.207.250 14:55, 29 August 2007 (UTC)

I'm not sure what it is that you are trying to say. It is definitely the case that log₂ 256 = 8. What is it that you mean? Xantharius 16:51, 29 August 2007 (UTC)

x is unknown

Quote: "In the context of a problem, a variable may represent a certain value of which is uncertain, but may be solved through the formulation and manipulation of equations". Does this make sense? What is "a certain value of which is uncertain"? Please improve the text. Bo Jacoby (talk) 13:06, 4 February 2008 (UTC).

I Need solved Papers —Preceding unsigned comment added by 203.199.41.181 (talk) 04:18, 28 August 2008 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Elementary algebra/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Examples of each. As this is aimed at High school level it could be made simpler. Salix alba (talk) 10:57, 22 April 2006 (UTC) The article as written is rather shoddy, and certainly doesn't meet the standards for a "good article" — Preceding unsigned comment added by 83.158.63.7 (talk) 13:52, 13 October 2011 (UTC)

Last edited at 13:53, 13 October 2011 (UTC). Substituted at 06:32, 7 May 2016 (UTC)