Timeline for What is it called when terms disappear when reducing fractions?
Current License: CC BY-SA 4.0
30 events
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| Sep 25, 2018 at 19:05 | comment | added | Bill Dubuque | @Dan The above discussion on "eliminate" vs. "cancel" is actually an offshoot of the discussion below Gerald's answer. I don't know why guest moved it here. | |
| Sep 21, 2018 at 5:10 | comment | added | Dan Fox | @guest: In English "eliminate" and "cancel" are not exact synonyms, in either ordinary or mathematical use. In mathematics, eliminate is mostly used in the context of solving systems of equations by eliminating variables (as in Gaussian elimination, or other more sophisticated kinds of elimination); this use is classical (19th century), but persists in some limited contexts, e.g. linear algebra. Cancellation is used with a less precise meaning, and generally refers to reciprocal elimination - some quantity is eliminated from both sides of the equation via multiplication by its inverse. | |
| S Sep 16, 2018 at 14:43 | history | edited | user52817 | CC BY-SA 4.0 |
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| Sep 15, 2018 at 18:51 | review | Suggested edits | |||
| S Sep 16, 2018 at 14:43 | |||||
| Sep 15, 2018 at 18:12 | comment | added | Bill Dubuque | @guest Thanks for following up. I suspected based on my experience that such usage would be rare. But it appears it is even rarer than I surmised. I was hoping that someone would find a few interesting examples that might shed some light on the scope and origins of such usage. | |
| Sep 15, 2018 at 15:22 | comment | added | guest | IOW, you seem to be right. | |
| Sep 15, 2018 at 4:31 | comment | added | guest | All right. I looked around and can't find any such use. It seems like documents (going back to the 1880s) seem to be very doctrinaire about using certain terms for certain operations. Cancel is used in context of fractions. Elimination in context of simultaneous equations. So I guess you are used to a certain term used for a certain operation. See where you are coming from, now, number. Just as a civilian, who uses words, it didn't seem strange to me since the words mean same thing, colloquially. But it does seem that algebra texts reserve the words to distinct topics. | |
| Sep 15, 2018 at 4:17 | comment | added | guest | And your initial comment did not ask for "eminent" and "respectable" web pages. You are moving the goal posts. | |
| Sep 15, 2018 at 4:15 | comment | added | guest | I was responding to you. And you did in fact make a claim and then dump the burden of proof on the opposite. | |
| Sep 15, 2018 at 3:20 | comment | added | Bill Dubuque | @guest Please give a link to a specific (reputable) web page and specific location on that page showing use of "eliminate" to mean "cancel". You haven't given even one such example (none in your first link).. It is your claim that such usage exists so it is your burden of proof, not mine. | |
| Sep 15, 2018 at 2:39 | comment | added | guest | google.com/… | |
| Sep 15, 2018 at 2:35 | comment | added | guest | 1. You only asked for one link to start. 2. A Google search (it is your friend) shows several others. 3. You continue to make a strong assertion of YOURS and then put burden of proof on others to disprove it. Go make your own survey! | |
| Sep 14, 2018 at 21:01 | comment | added | Bill Dubuque | @guest You have yet to provide even one link to a page that uses "eliminate" to mean "cancel", let alone one in a reputable publication (as I requested). | |
| Sep 14, 2018 at 20:28 | comment | added | guest | A Google search comes up with plenty more examples. And I am personally familiar with either term being used. So...burden of proof on you, if you want to advocate the opposite. | |
| Sep 14, 2018 at 19:44 | comment | added | Bill Dubuque | @jpmc26 As I explained above it depends on the context (which is missing in the OP). The contexts I refer to do not require expert-level knowledge of mathematics. | |
| Sep 14, 2018 at 19:30 | comment | added | jpmc26 | @Number See point 3. We know for a fact that our audience does not consist of expert mathematicians that will instantly recognize the limitation. | |
| Sep 14, 2018 at 18:34 | comment | added | Bill Dubuque | @jpmc26 While I agree that such attention to detail is important in some contexts, it's not clear that is the case here. In some contexts there is no need to append the proviso $b\neq 0$ to the result, e.g. if our context is algebra (vs. analysis) where $f := f(x)$ denotes a polynomial then $ f = x^2/x\,\Rightarrow\, f = x$ is true even when $x=0$. In other contexts there may be ambient conventions in use that appropriately account for singularities. | |
| Sep 14, 2018 at 18:24 | comment | added | Bill Dubuque | @guest One can find all sorts of nonsense on random web pages. I was hoping for links to use by eminent authors, e.g. a professional algebraist. | |
| Sep 14, 2018 at 18:11 | comment | added | guest | liguistically I understand cancel and eliminate as same thing. Doesn't even give me pause. ceemrr.com/Geometry2/Eliminating_Fractions/… (many other examples available...GIYF) | |
| Sep 14, 2018 at 18:01 | comment | added | jpmc26 | @Number 1. Once you cancel it, it's not obvious there is a denominator. Stating the restriction explicitly makes it more clear that the condition applies to everything that follows. 2. $b$ may not have been defined as a denominator. The restriction still applies to conclusions that follow. 3. As this is an educator site, it's important to note that students can easily miss this important detail. 4. Depending on the starting equations, $b = 0$ may yield some other solution that needs to be found. Keeping in mind that this one doesn't work for that case helps you remember to look for it. | |
| Sep 14, 2018 at 17:58 | answer | added | Xander Henderson♦ | timeline score: 3 | |
| Sep 14, 2018 at 17:54 | comment | added | Bill Dubuque | @jpmc26 Denominators of fractions are nonzero by definition. | |
| Sep 14, 2018 at 17:23 | comment | added | jpmc26 | Note that your solution is incomplete. You are still left with the condition $ b \ne 0$ that must be tacked onto every conclusion that follows. | |
| Sep 14, 2018 at 16:13 | answer | added | Milo Brandt | timeline score: 8 | |
| Sep 14, 2018 at 15:35 | comment | added | Bill Dubuque | Simpler: $\color{#c00}{b^{-1}} x = \color{#c00}{b^{-1}} c\,\Rightarrow\, x=c\,$ by cancelling $\,\color{#c00}{b^{-1}},$ i.e. we can apply the Cancellation Law (rather than repeating its proof inline) | |
| Sep 14, 2018 at 12:29 | answer | added | Gerald Edgar | timeline score: 13 | |
| Sep 14, 2018 at 10:15 | vote | accept | AndreKR | ||
| Sep 14, 2018 at 9:57 | answer | added | JRN | timeline score: 10 | |
| Sep 14, 2018 at 9:40 | review | First posts | |||
| Sep 14, 2018 at 15:35 | |||||
| Sep 14, 2018 at 9:36 | history | asked | AndreKR | CC BY-SA 4.0 |