Timeline for Why is distribution prioritized over combining?
Current License: CC BY-SA 4.0
23 events
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| Apr 17, 2021 at 16:06 | history | edited | Tommi | CC BY-SA 4.0 |
removed old edit notices, inappropriate tag
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| Apr 17, 2021 at 15:10 | history | edited | Daniel R. Collins | CC BY-SA 4.0 |
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| Dec 22, 2019 at 21:29 | history | edited | Daniel R. Collins | CC BY-SA 4.0 |
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| Dec 22, 2019 at 21:28 | vote | accept | Daniel R. Collins | ||
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Sep 14, 2015 at 20:41 | answer | added | Thinkeye | timeline score: 2 | |
| Sep 13, 2015 at 21:51 | answer | added | Benjamin Dickman | timeline score: 9 | |
| Sep 12, 2015 at 10:33 | answer | added | vonbrand | timeline score: 3 | |
| Sep 12, 2015 at 5:59 | history | edited | Daniel R. Collins | CC BY-SA 3.0 |
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| Sep 12, 2015 at 5:59 | comment | added | Daniel R. Collins | Edited the OP to clarify that the principle of similitude reference is only in reference to the motivating unit analogy. | |
| Sep 12, 2015 at 2:03 | comment | added | Daniel R. Collins | Add deleted the cross-post on MathOverflow. | |
| Sep 12, 2015 at 2:03 | history | edited | Daniel R. Collins | CC BY-SA 3.0 |
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| Sep 12, 2015 at 1:52 | comment | added | Daniel R. Collins | I've edited the OP to add links to the site cross-posts; thanks Zev. | |
| Sep 12, 2015 at 1:51 | history | edited | Daniel R. Collins | CC BY-SA 3.0 |
Added links to site cross-posts
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| Sep 11, 2015 at 6:07 | comment | added | Zev Chonoles | Note: now crossposted at both Math.SE (math.stackexchange.com/q/1417856/264) and MathOverflow (mathoverflow.net/q/218003/1916). | |
| Sep 7, 2015 at 23:55 | comment | added | Alexander Woo | Changing every instance of $a(b+c)$ to $ab+ac$ (in a polynomial) can be done "mechanically". However, changing instances of $ab+ac$ to $a(b+c)$ requires one to recognize when terms have common factors, and incompatible choices may be involved. (When you have $ab+bc+cd$, either of two combining operations, but not both, can be applied.) Hence the normal form for polynomials (in any number of variables) is the unfactored form. | |
| Sep 5, 2015 at 20:17 | comment | added | Daniel R. Collins | I agree with Steven that trying to overturn this standard presentation would be a monumental undertaking, but I can't even track down any history or justification for why we do it the way we do. So my outstanding question is if there's some historical reason, or higher-level abstract algebraic property, for picking option (1). | |
| Sep 5, 2015 at 20:15 | comment | added | Daniel R. Collins | Steven Gubkin has my meaning; I'm talking about both the order of the presentation and the name itself. Granted that (a) we will take one as axiomatic, and (b) the initial emphasis will be on the left-to-right transformation (and so the name is inherently connected to the initial presentation and application), then it seems that we had two options. Option (1) "distribution" a(b+c) = ac+bc; option (2) "combining" (or collection) ac+bc = (a+b)c. It seems like option (2) is far more intuitive and commonsensical and so easier to digest as an axiom. | |
| Sep 5, 2015 at 18:58 | comment | added | Steven Gubkin | I think it is probably just a historical accident. As soon as you have the name "distributivity" for the law in question, people will want to write it in the form $a(b+c) = ab+ac$, to demonstrate the $a$ being distributed to the $b$ and $c$. We have a verb "distributing", but using the verb "combining" is less standard. Changing the language will probably be difficult, even if it does make a little more sense. I would also like to write function composition in the other order, but we do not live in a perfect world. But feel free to write the equality the other way when you teach it. | |
| Sep 5, 2015 at 12:10 | comment | added | Joonas Ilmavirta | I think it would be good to emphasize early on that equations work both ways. Some students who remember $(x+y)^2=x^2+2xy+y^2$ fluently don't recognize that $x^2+2xy+y^2$ could be written as a square, especially if $x$ and $y$ are more complicated than a single variable. Too often have I heard people say "it never occurred to me that you could use this identity in that direction". Making students see "$=$" as a symmetric binary relation should make distribution and combining obviously equivalent for the students. | |
| Sep 5, 2015 at 11:41 | review | Close votes | |||
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| Sep 5, 2015 at 8:09 | comment | added | Benjamin Dickman | I'm having a bit of trouble parsing your question. Are you asking about why the left-hand side of this equality is typically presented as $a(b+c)$ and the right-hand side as $ab + ac$, whereas presenting them in a switched order seems more natural, to you, pedagogically? As in, you would prefer it written as: $ab + ac = a(b+c)$? (In your examples, you have distribution occurring on different sides of the parenthetical sum, and you've also changed from $a, b, c$ to $a, b, x$...) | |
| Sep 5, 2015 at 5:59 | history | asked | Daniel R. Collins | CC BY-SA 3.0 |