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I have added a second definition to the lead, covering the sense of "divisor" to as at the start of the Terminology section. I don't actually agree with my own addition: an article should be about a concept, and should not cover two independent concepts that happen to share the same name. I think that this article should cover only the sense in abstract algebra (possibly restricted to integers), with a hatnote with a redirect to the other sense. To get rid of the alternative definition will involve removing a few lines only. Comment? — Quondum 22:53, 1 August 2013 (UTC)
The question of whether or not zero is a divisor of zero has reappeared at the Math Project Talk page. The question interested me enough to go scrambling through a number of texts (algebra, number theory, intro to proofs). I found both sides of the issue equally represented. About half define a | b only for nonzero a. About half of those that permit a to be zero make no statement about 0 | 0, while the rest are quite explicit about this being true. The authors ran the gamut and included some very respectable mathematicians. Some quick examples:
The one thing that I did not find was any statement about uniqueness in the definition of divisor. Personally I kind of like that wrinkle in the definition and it may appear in some education literature, but I don't have a citation for it.
The current definition on this page only reflects one point of view on the issue and probably should be expanded to give a broader perspective. Bill Cherowitzo ( talk) 04:01, 2 August 2013 (UTC)
With such encouragement I have edited the page in line with my previous comments. As to my choice of order in the definition, this version required the fewest number of changes/comments in the rest of the article (3) and avoided a nasty one in the definition of trivial divisors. Bill Cherowitzo ( talk) 20:01, 5 August 2013 (UTC)
A recent edit cleanly removed the exclusion of 0 as a divisor, but in so doing going against the consensus to represent both of the prevalent definitions. I do not wish to revert this, because I think it would make sense to reintroduce the exclusion as a modification of the less restrictive case (i.e make it the second definition). This will improve readability. It will also make dealing with my "subtle point" easier as a later caveat, rather than something extra to be "forgotten" when removing the zero exclusion. — Quondum 17:52, 27 October 2013 (UTC)
I am teaching some remedial math, and point students to wikipedia sometimes. Sending them here to learn the meaning of divisor would be a mistake; this page apparently deals with integer divisors, but the term is more general. I think a sentence briefly explaining this, with a link to the page on division would improve this page (see also the first comment by "mirwin" and the "wow" comment above). — Preceding unsigned comment added by 76.103.108.10 ( talk) 21:27, 3 April 2014 (UTC)
The current article focuses only on the definition of divisor restricted to the field (er, ring) of integers. The section "Definition" states "Two versions of the definition of a divisor are commonplace".
This is patently silly. The word "divisor" is commonly used to refer to the "number on the bottom of a division", as it is in Wikipedia's own Long division article. "As in all division problems, one number, called the dividend, is divided by another, called the *divisor*, producing a result called the quotient."
One can appreciate that there are more restricted uses of a word in certain technical or academic realms. That does not mean that these realms dictate the meaning of the word over all other uses. This should be pointed out in the introduction. If a discussion of the more-specialized meaning is valuable, then it should be accompanied by an indication that it's a more specialized meaning.
This is, after all, the article titled "Divisor", not titled "Divisor (within mathematics, narrowly construed)" Gwideman ( talk) 23:18, 11 November 2015 (UTC)
"a divides b" is abbreviated a|b
Is there an abbreviation for "a does not divide b"? 2.24.119.101 ( talk) 17:23, 1 December 2015 (UTC)
This article shows why the civilian world has such a problem with math. If I ever go to hell I expect that I will be forced to read this article every day, and I *am* a mathematician. Something as basic as divisor shouldn't require a PhD to understand, or two minutes to figure it out from the noise.
I really hoped I could simply find the following sentence way up top in the article. Maybe even as a paragraph right above the table of contents. I submit this for consideration.
Simply speaking, for the equation c equals a divided by b (c=a/b), c is the quotient, a is the dividend, and b is the divisor.
Perhaps "Simply" could be "Generally".
If you just put that in the intro paragraph, not only will the suicide rate decline among math students, but the time it takes to simply see "which one is called the divisor" will be reduced to - a mere fraction. 24.27.72.99 ( talk) 04:27, 10 August 2017 (UTC)
EDIT: I apologize for not responding earlier, David Eppstein. You are technically correct, in point of fact...yet...
I hope you'll agree, though, that the poorly assigned article title simply begs for this interpretation. Why in the WORLD would the article title state a general term ("divisor") - yet then discuss it only in a rare and limited usage? That's like titling an article "Red (color)" then only discussing the color "carmine" in the article, saying, "for mainstream use of the color 'red' see some other article." I believe that 99% of third grade arithmetic teachers would assert that the word divisor does not mean "the integer math subset meaning of the word."
This article is horribly mistitled :( 76.185.10.9 ( talk) 15:57, 27 March 2018 (UTC)
Oh come on. If I want to find out what "divisor" means, I'm not going to search for division. Seriously? If someone want to find out what "divisor" means, "divisor" is the first word that someone looks up. 2600:6C56:6600:1EA7:694D:FA90:265A:6C39 ( talk) 13:53, 17 January 2019 (UTC)
I am on firefox 56.0.1 (64-bit) on Win 7 and I get this red text on the page: Screenshot I have no idea what it is and what it means, so can someone fix it? Thanks, 79.101.241.42 ( talk) 19:10, 25 October 2017 (UTC)
It seems to me that both definitions in the article as stated allow 0 | 0, and that where they differ is whether or not nonzero integers also divide zero. So I made some edits reflecting this. However, I notice that there are several footnotes in the article pointing out facts that require 0 | 0 to be true. Are there other common definitions that do not define divisibility when 0 is involved at all? Double sharp ( talk) 03:46, 4 February 2019 (UTC)
I have edited the article before reading this thread. In fact, in number theory, zero is always excluded, when considering divisibility. So, there is no reason to give so much emphasis on divisibility of and by zero, and to consider the two definition as of equal importance. D.Lazard ( talk) 10:59, 4 February 2019 (UTC)
Hi all, came here to check what a divisor and dividend is, wasn't entirely certain which was which. I expected to find a really simple description of "in a/b (or equivalently a÷b) then b is the divisor and a is the dividend". This is a superficial definition because it's purely a notational artefact, but still IMO useful. Thoughts? 79.75.100.60 ( talk) 11:45, 8 September 2020 (UTC)
Added: just noticed someone's made a similar point < /info/en/?search=Talk:Divisor#Complex!> For a simple operation, a simple (even if facile) description should be available. And BTW I didn't know that in this example, c was called the quotient. — Preceding unsigned comment added by 79.75.100.60 ( talk) 11:48, 8 September 2020 (UTC)
PLEASE...put this: "INTEGER ARITHMETIC ONLY" in the title. I read half the article thinking someone had lost their mind before looking up and seeing the italicized portion at the top. Please. Lots of people will walk away confused if they miss the easily overlooked italics. N0w8st8s ( talk) 17:49, 3 November 2020 (UTC)
This
level-5 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
This page has archives. Sections older than 365 days may be automatically archived by Lowercase sigmabot III when more than 10 sections are present. |
I have added a second definition to the lead, covering the sense of "divisor" to as at the start of the Terminology section. I don't actually agree with my own addition: an article should be about a concept, and should not cover two independent concepts that happen to share the same name. I think that this article should cover only the sense in abstract algebra (possibly restricted to integers), with a hatnote with a redirect to the other sense. To get rid of the alternative definition will involve removing a few lines only. Comment? — Quondum 22:53, 1 August 2013 (UTC)
The question of whether or not zero is a divisor of zero has reappeared at the Math Project Talk page. The question interested me enough to go scrambling through a number of texts (algebra, number theory, intro to proofs). I found both sides of the issue equally represented. About half define a | b only for nonzero a. About half of those that permit a to be zero make no statement about 0 | 0, while the rest are quite explicit about this being true. The authors ran the gamut and included some very respectable mathematicians. Some quick examples:
The one thing that I did not find was any statement about uniqueness in the definition of divisor. Personally I kind of like that wrinkle in the definition and it may appear in some education literature, but I don't have a citation for it.
The current definition on this page only reflects one point of view on the issue and probably should be expanded to give a broader perspective. Bill Cherowitzo ( talk) 04:01, 2 August 2013 (UTC)
With such encouragement I have edited the page in line with my previous comments. As to my choice of order in the definition, this version required the fewest number of changes/comments in the rest of the article (3) and avoided a nasty one in the definition of trivial divisors. Bill Cherowitzo ( talk) 20:01, 5 August 2013 (UTC)
A recent edit cleanly removed the exclusion of 0 as a divisor, but in so doing going against the consensus to represent both of the prevalent definitions. I do not wish to revert this, because I think it would make sense to reintroduce the exclusion as a modification of the less restrictive case (i.e make it the second definition). This will improve readability. It will also make dealing with my "subtle point" easier as a later caveat, rather than something extra to be "forgotten" when removing the zero exclusion. — Quondum 17:52, 27 October 2013 (UTC)
I am teaching some remedial math, and point students to wikipedia sometimes. Sending them here to learn the meaning of divisor would be a mistake; this page apparently deals with integer divisors, but the term is more general. I think a sentence briefly explaining this, with a link to the page on division would improve this page (see also the first comment by "mirwin" and the "wow" comment above). — Preceding unsigned comment added by 76.103.108.10 ( talk) 21:27, 3 April 2014 (UTC)
The current article focuses only on the definition of divisor restricted to the field (er, ring) of integers. The section "Definition" states "Two versions of the definition of a divisor are commonplace".
This is patently silly. The word "divisor" is commonly used to refer to the "number on the bottom of a division", as it is in Wikipedia's own Long division article. "As in all division problems, one number, called the dividend, is divided by another, called the *divisor*, producing a result called the quotient."
One can appreciate that there are more restricted uses of a word in certain technical or academic realms. That does not mean that these realms dictate the meaning of the word over all other uses. This should be pointed out in the introduction. If a discussion of the more-specialized meaning is valuable, then it should be accompanied by an indication that it's a more specialized meaning.
This is, after all, the article titled "Divisor", not titled "Divisor (within mathematics, narrowly construed)" Gwideman ( talk) 23:18, 11 November 2015 (UTC)
"a divides b" is abbreviated a|b
Is there an abbreviation for "a does not divide b"? 2.24.119.101 ( talk) 17:23, 1 December 2015 (UTC)
This article shows why the civilian world has such a problem with math. If I ever go to hell I expect that I will be forced to read this article every day, and I *am* a mathematician. Something as basic as divisor shouldn't require a PhD to understand, or two minutes to figure it out from the noise.
I really hoped I could simply find the following sentence way up top in the article. Maybe even as a paragraph right above the table of contents. I submit this for consideration.
Simply speaking, for the equation c equals a divided by b (c=a/b), c is the quotient, a is the dividend, and b is the divisor.
Perhaps "Simply" could be "Generally".
If you just put that in the intro paragraph, not only will the suicide rate decline among math students, but the time it takes to simply see "which one is called the divisor" will be reduced to - a mere fraction. 24.27.72.99 ( talk) 04:27, 10 August 2017 (UTC)
EDIT: I apologize for not responding earlier, David Eppstein. You are technically correct, in point of fact...yet...
I hope you'll agree, though, that the poorly assigned article title simply begs for this interpretation. Why in the WORLD would the article title state a general term ("divisor") - yet then discuss it only in a rare and limited usage? That's like titling an article "Red (color)" then only discussing the color "carmine" in the article, saying, "for mainstream use of the color 'red' see some other article." I believe that 99% of third grade arithmetic teachers would assert that the word divisor does not mean "the integer math subset meaning of the word."
This article is horribly mistitled :( 76.185.10.9 ( talk) 15:57, 27 March 2018 (UTC)
Oh come on. If I want to find out what "divisor" means, I'm not going to search for division. Seriously? If someone want to find out what "divisor" means, "divisor" is the first word that someone looks up. 2600:6C56:6600:1EA7:694D:FA90:265A:6C39 ( talk) 13:53, 17 January 2019 (UTC)
I am on firefox 56.0.1 (64-bit) on Win 7 and I get this red text on the page: Screenshot I have no idea what it is and what it means, so can someone fix it? Thanks, 79.101.241.42 ( talk) 19:10, 25 October 2017 (UTC)
It seems to me that both definitions in the article as stated allow 0 | 0, and that where they differ is whether or not nonzero integers also divide zero. So I made some edits reflecting this. However, I notice that there are several footnotes in the article pointing out facts that require 0 | 0 to be true. Are there other common definitions that do not define divisibility when 0 is involved at all? Double sharp ( talk) 03:46, 4 February 2019 (UTC)
I have edited the article before reading this thread. In fact, in number theory, zero is always excluded, when considering divisibility. So, there is no reason to give so much emphasis on divisibility of and by zero, and to consider the two definition as of equal importance. D.Lazard ( talk) 10:59, 4 February 2019 (UTC)
Hi all, came here to check what a divisor and dividend is, wasn't entirely certain which was which. I expected to find a really simple description of "in a/b (or equivalently a÷b) then b is the divisor and a is the dividend". This is a superficial definition because it's purely a notational artefact, but still IMO useful. Thoughts? 79.75.100.60 ( talk) 11:45, 8 September 2020 (UTC)
Added: just noticed someone's made a similar point < /info/en/?search=Talk:Divisor#Complex!> For a simple operation, a simple (even if facile) description should be available. And BTW I didn't know that in this example, c was called the quotient. — Preceding unsigned comment added by 79.75.100.60 ( talk) 11:48, 8 September 2020 (UTC)
PLEASE...put this: "INTEGER ARITHMETIC ONLY" in the title. I read half the article thinking someone had lost their mind before looking up and seeing the italicized portion at the top. Please. Lots of people will walk away confused if they miss the easily overlooked italics. N0w8st8s ( talk) 17:49, 3 November 2020 (UTC)