Talk:Remainder

message: Such as number modulo 3 := sum of the digits (decimal base)
Example: 62837 mod 3 = 6+2+8+3+7 mod 3 = 26 mod 3 = 2+6 mod 3 = 8 mod 3 = 2
Another: number modulo 7 := number lest the last digit - 2 * last digit (decimal base)
Example: 62837 mod 7 = 6283-14 mod 7 = 6269 mod 7 = 626-18 mod 7 = 608 mod 7 = 60-16 mod 7 = 44 mod 7 = 2
Ïnteresting would be an algorithm for numbers modulo 31; with that you could calculate in your head certain check digits to forge a social security number in situ...
:There already is an article about this: Divisibility rule. I will add this to the "see also" section. 93.95.251.162 (talk) 11:46, 15 March 2011 (UTC)
thread_title: Remainder algorithms for various moduli

message: To say "it can be proved" is correct English. See for example this Britannica article. For some reason, it sounds more natural to my ear than "it can be proven". That's why I will change this in remainder.Oleg Alexandrov 05:07, 10 Mar 2005 (UTC)
replies: text: OK. I think this is one of those situations where what is correct and what sounds natural are sometimes different things, depending on regional dialects. I asked several people and got several answers. Everyone felt "proved" was right, but they also all hesitated and conceded that they hear "proven" used in that context just as often. - mjb 01:48, 11 Mar 2005 (UTC)
replies: text:  I see. If you feel strongly about it, you can revert to "proven". I am not a native speaker, and ultimately I can't know for sure. Oleg Alexandrov 02:08, 11 Mar 2005 (UTC)
thread_title: Proven or proved

message: Can we discuss this before getting carried away with the edits today? — mjb 22:51, 11 May 2005 (UTC)
replies: text: You mean the removal of ×? I don't care either way. But, since Michael Hardy removed one occurance, I thought to remove all of them for consistency. Oleg Alexandrov 23:02, 11 May 2005 (UTC)
replies: text: Yeah, I thought you were going to remove every single instance of ×, which wouldn't be appropriate, in my opinion (see below). mjb 23:25, 11 May 2005 (UTC)

text: I myself don't care. :) I asked Michael Hardy to comment on this. Oleg Alexandrov 23:46, 11 May 2005 (UTC)

text: Yes! Oleg Alexandrov 23:46, 11 May 2005 (UTC)
thread_title:  Formula formatting 

message: Regarding   or  )… the pros are that it
* prevents formulas from wrapping, and
* improves readability.
The cons are that:
* Wikipedia gets confused sometimes and adds an extra space, such as the one before the d in x < r ≤ x + |d| (there is no space there in the original code); and this seems to have gone away in a recent MediaWiki upgrade
* there are no clear rules on when and how to use them.
Is the formatting bug something you can live with? Is there a workaround?
: I myself don't care. :) I asked Michael Hardy to comment on this. Oleg Alexandrov 23:46, 11 May 2005 (UTC)
thread_title:  No-break space 

message: I think it is reasonable to assume that standard algebraic notation is best for formulas, so two variables q and d being multiplied are probably best written as qd when presented in a formula. That is, when citing a formula, don't use ×.
However, when explaining, for a general audience (not just mathematicians), the formula or giving examples of its application, I feel it is prudent to use the multiplication sign — "×", coded as ×. So, I think these examples should remain as-is (although I added no-break spaces here):
* When dividing 26 by 4, 6 is the quotient and 2 is the remainder, because 26 = 6 × 4 + 2.
* −42 = 9 × (−5) + 3
Do others agree with this convention?
: Yes! Oleg Alexandrov 23:46, 11 May 2005 (UTC)
thread_title:  Multiplication sign 

message: Grammar question:
* 2 is the remainder after division of 26 by 4.
* 2 is the remainder of division of 26 by 4.
Is either one acceptable? Does one sound better than the other? — mjb 08:56, 9 August 2005 (UTC)
thread_title:  Remainder 'after' or 'of' division 

message: In the article today
−42 = 9×(−5) + 3
seems to be saying -42 divided by -5 has a quotient of 9 with a remainder 3.
This may be true, based on the article definition, but I'm not sure we should accept that.  I think most people would accept that ±42 divided by ±5 would give some kind of 8 as a quotient, not a 9.  Additionally, the article definition of remainder does not allow the ambiguity introduced in the section with the word ambiguity.  Isn't THAT ambiguous?  Something needs to be changed!  I vote we find an actual source for the definition of remainder.  75.17.12.230 07:58, 8 September 2007 (UTC)
thread_title:  Negatives 

message: I've seen the phrase "divides into" in print before, as in "a does not divide into b", referring to the fact the remainder of a/b is nonzero.
Alternatively, "divides evenly by" is used sometimes to the same effect.
Could there be a place for this information either in this article or in Division (mathematics)#Notation or Multiple (mathematics)?  —Preceding unsigned comment added by Kostmo (talk • contribs) 05:12, 15 February 2009 (UTC)
thread_title:  colloquial phrases? 

message: There are some other definitions of remainder that should be considered in this article:
#the result of a subtraction (historical)
#the amount left over after any stage of a long division
#the residual after polynomial long division
#the expression for the truncation error in Taylor's theorem.
I have been adding article links and references for these subjects. RockMagnetist (talk) 18:58, 29 January 2013 (UTC)
thread_title:  Other meanings 

message: I've written and edited middle school maths textbooks for students on two continents and taught post-high school maths on a third, and I've yet to encounter residue in a mathematical sense. Where is this used? Thanks.
--Unicorn Tapestry {say} 14:48, 18 August 2013 (UTC)
replies: text: One use is simply as a synonym for remainder. See Residue for some more mathematical meanings. RockMagnetist (talk) 20:20, 18 August 2013 (UTC)
replies: text: Thanks, Rock, but that's kind of a circular definition. Where, other than Wikipedia, is 'residue' used as a synonym for 'remainder'? If we can't document, we shouldn't use it. Thanks. --Unicorn Tapestry {say} 05:27, 25 August 2013 (UTC)
replies: text: A google and perusal of the first 20 entries of division and residue turns up mostly references to residue number systems, a question about 'residue', and a description of modulo arithmetic, which discusses remainder and 'residual', not residue. Unless something more definitive arises, I suggest we delete this until more evidence comes along. --Unicorn Tapestry {say} 05:27, 25 August 2013 (UTC)
thread_title:  Residue? 

message: The starting paragraph
:"In arithmetic, the remainder (or modulus) is the amount "left over" after performing the division of two integers which do not divide evenly, that is, where the result of the division cannot be expressed as an integer."
does not seem quite right since the remainder could be zero: 8/2 is an integer, 8 divided by 2 has remainder 0.
This early definition contradicts what is later explained in the page:
:"If a and d are natural numbers, with d non-zero, it can be proven that there exist unique integers q and r, such that a = qd + r and 0 ≤ r < d. The number q is called the quotient, while r is called the remainder..."
and
:"If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with |r| < |d|."  — Preceding unsigned comment added by Nestor.aguilera (talk • contribs) 21:49, 7 February 2014 (UTC)
thread_title:  informal introductory definition 

message: 🥺 2409:4042:269F:45F7:8CC8:F7B7:B350:614E (talk) 09:11, 19 April 2022 (UTC)
thread_title:  BLACK DAY 11 APRIL