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This article needs to be fixed. The way it's written a and c are points while b is a distance. This is not a proper geometric analogy to the way subtraction is carried out, and the original writer is subtracting two different classes of objects.
Perhaps you've heard it mentioned that you can't add or subtract apples and oranges 1) Start with 3 apples
2) Take away 2 oranges from those 3 apples
3) One shouldn't expect to have 1 apple left, as subtraction in this way just doesn't make sense.
Points are quite different than distances, and just as in the case with apples and oranges, one should not expect to be able to subtract distances from points. Instead a, b, and c should all be distances from the origin, a point who's numerical value is zero. In this way the distance to c minus the distance to a is the distance b.
Could somebody who posesses both the tools to generate decent images as well as a strong math background fix this article? - User:AlfredR
AlfredR is misinformed, and I'm going to restore jaredwf's Basic subtraction section. I'm also going to give a lengthy argument here on the talk page, because the good name of mathematics itself is at stake, and becuase I have nothing better to do.
Geometric vectors (in our case, signed distances) are equivalence classes of "differences of points"; they are exactly the correct objects to add to, or subtract from, points. We need not summon the chimeras that are "position vectors". In some sense, it is more fundamental to subtract a vector from a point than from another vector.
On a more general note, the apples-and-oranges analogy is worse than wrong. Teenagers don't even blink if you subtract the number 2 from the letter x. No one complains if I multiply a matrix with a column vector or an algebraic number with a spinor field. Half the fun of geometric algebra is adding quantities with different dimensions, and hang the taboos. Some of the most interesting mathematics arises when fundamentally different objects interact and when familiar concepts are revealed to tolerate a whole lot more ambiguity than they let you know about in school. Moral: mathematicians are clever. If you think something is meaningless, they will give it meaning.
(By the way, if we make the usual assumption that apples and oranges are unrelated, then 3 apples minus 2 oranges is an element in the free abelian group over apples and oranges. If, for some application, we later find it useful to equate apples and oranges, we can pass to the quotient group by this equivalence through the canonical projection and, yes Virginia, we will have one apple left.)
Now that I'm done ranting, I should comment that the section in question is a little unencyclopedic in tone. It should be condensed or rewritten, but not deleted. Melchoir 10:34, 27 November 2005 (UTC)
AlfredR 21:37, 3 October 2006
P.S. If there are 3 apples and you take away 2, you have 2 because you took them. -- 116.14.26.124 ( talk) 01:15, 23 June 2009 (UTC)
Please explain this. It starts out as 100-11, then jumps to 90-11=79, which in no way answers 100-11=(89). I may be completely confused. Oh yeah, and please don't go into vectors, I mean this is a Subtraction page, and while that is possible, the page links to Arithmetic and Elementary School! Chrishy man 02:59, 4 April 2007 (UTC)
I made a substantial edit. Apologies if I stepped on anyone's toes. My motivation is that a lot of parents need to know about the differences in American-style and European-style carries. This is a major problem for parents when their kids come home from school with a subtraction style different than the one the parents know. I also wanted to document the history of the subtraction methods. I am sure that the education literature is full of comments here. Thanks for everyone's patience. -- Ozga 16:21, 23 August 2007 (UTC)
Currently this article has nothing at all about subtraction of objects other than numbers. Perhaps links to other things (on wikipedia) that have subtraction operators defined could be added. InformationSpace 06:45, 19 June 2007 (UTC)
Usually when teachers teach their class, there are several items. The student usually Xs out the apples. —Preceding unsigned comment added by Pkkao ( talk • contribs) 01:26, 8 July 2007
In this article, difference is described as "the restult of subtraction". Is it actually the result of subtraction, or the positive result? Take for example The difference of 2 and 3 = 3 - 2 = 1, then The diference of 3 and 2 = 2 - 3 = -1 or |2 - 3| = 1 ? —Preceding unsigned comment added by 137.222.234.90 ( talk) 06:37, 12 October 2007 (UTC)
Multiple meanings of "difference" can be annoying or confusing and maybe ought to be pointed out by someone more mathematical than me however as I understand it this is not "negative difference" but instead the difference between the "difference as comparison" and the "difference as subtraction result" where the difference (comparison) between {5, 14} as well as {14, 5} are equivalent and 9 (the comparison in this case is in each set the gap on the number line and they give the same result in both directions from one to the other) and the difference (result of subtraction) where the difference of 5-14 = -9 (14 places less than 5 on the number line) in the first set or in the second set 14-5 = 9 (5 places less than 14) and where both sets give different results and one of them is the same result as the comparative difference. One might have to take extra care to avoid ambiguity when writing descriptive verbose math explanations such as "two even factors produce an even product, and subtracting two from the product leaves an even difference" (for those interested this is part of my (possibly wrong or poorly written) answer to question 7 in Exercises 1.1. in "An Introduction to Combinatorics and Graph Theory" which is a CC by-nc-sa licensed maths textbook). 90.149.36.98 ( talk) 23:29, 26 July 2018 (UTC)
Subtraction simply reverses movement on the line of real numbers, does it not? This is especially comprehendable when subtraction is viewed as addition (as in algebra.) Consider:
5-3=2 backward movement of |3| on the number line.
5-(-3)=8 forward movement of |3) on the number line; that is to say, the "-" immediately proceeding "5" is reversing the operation that would otherwise be done if it was only "-3": addition. Children in junior-high often say this as "minus a minus."
What I am saying is very obvious, but subtraction defined as "reversing movement on the line of real numbers" is an all-encompassing definition that would cover both the algebraic and arithmetic understanding of subtraction. This has probably been said and proven somewhere in academia, but perhaps we could place it on Wikipedia. —Preceding unsigned comment added by CPRdave ( talk • contribs) 01:07, 26 October 2007 (UTC)
The article should state that subtraction is the inverse of addition. The subtraction of a number from itself gives 0, the identity element for addition. For a given element a of an additive group, the inverse -a is unique. This should also be in the article IMHO. John ( talk) 16:34, 25 June 2014 (UTC)
I applaud the work of the person who took the time to carefully explain how subtraction works despite there being no one who can read this article and not subtract. :) -- MQDuck 07:45, 4 March 2009 (UTC)
Is that "citation needed" tag after the explanation of the terms minuend and subtrahend really necessary? It is surely common sense to assume that these particular words are seldom used in mathematical parlance. -- T.M.M. Dowd ( talk) 23:49, 1 January 2010 (UTC)
Subscript text 224,940-175,000= to —Preceding unsigned comment added by 121.1.53.54 ( talk) 23:33, 19 February 2010 (UTC)
It would be nice if a section on the problem of precision loss in limited-precision subtraction (if numbers are subtracted that are much larger than their difference) and on common workarounds could be added. As this is probably the most important source of precision loss in real-world algorithms. -- 92.229.180.109 ( talk) 13:58, 22 March 2010 (UTC)
I take some issue with this article. "Minuend" and "subtrahend" are commonly used in computer science as well as discussion of arithmetic. However, some editor of this article has made the effort to elevate the assertion:
While this point is arguable, I question that it should appear:
Heathhunnicutt ( talk) 17:41, 12 June 2010 (UTC)
Subtrahend is certainly not an archaic term. (I'm in agreement with Heathhunnicutt.) "Subtrahend" is a specific entity that refers to the value (or item that contains the value) by which another value will be decreased. It's taught in Computer Science, Engineering, and Mathematics courses. Even 2nd grade Math (where U.S. students are generally about 8 years old) are taught the meaning of "subtrahend". And to cite a satirical work as a reference suggests that the poster is having fun, or on a personal agenda. — Preceding unsigned comment added by KentOlsen ( talk • contribs) 18:48, 8 December 2011 (UTC)
The article currently states that "some" American schools teach the borrowing method. As far as I know it is virtually universal in American schools. Can any-one find a citation so we can beef up the statement to reflect reality? Kdammers ( talk) 03:10, 9 January 2013 (UTC)
"In mathematics, it is often useful to view or even define subtraction as a kind of addition, the addition of the additive inverse. We can view 7 − 3 = 4 as the sum of two terms: 7 and -3. This perspective allows us to apply to subtraction all of the familiar rules and nomenclature of addition. Subtraction is not associative or commutative—in fact, it is anticommutative and left-associative—but addition of signed numbers is both." the first part makes the "naive" reader think that subtraction should be associative ("allows us to apply to subtraction all of the familiar rules ... of addition"), but this is followed -- with-out a "however" and only a delayed "in fact"-- by a sentence that says "Subtraction is not associative...." This makes for unnecessarily tough reading. Kdammers ( talk) 03:15, 9 January 2013 (UTC)
The article states that "… crutches are apparently the invention of William A. Brownell who used them in a study in November 1937." This is clearly false. See ref 1, which I just added for "crutches" and the Austrian method. You can read it on google books, click on the link. This is a book published in 1916 by an American, Paul Klapper. He talks about crutches and their usage in subtraction algorithms at least 21 years before Brownell's article. John ( talk) 04:01, 24 June 2014 (UTC)
I went to the library and looked up the article by Brownell by looking in the comprehensive index of the journal, The Mathematics Teacher. The text is wrong, his essay appears in vol. 37, year 1945 (not 1937) of The Mathematics Teacher. There is no mention of crutches. So the statement about Brownell has two errors. I'm rewriting the paragraph. John ( talk) 00:48, 25 June 2014 (UTC)
Correction: it was the wrong article. Brownell conducted his study in 1937. It was apparently published in 1949, according to Susan C. Ross and Mary Pratt-Cotter, Subtraction From a Historical Perspective, published in 2010. — Preceding unsigned comment added by John Palkovic ( talk • contribs) 00:58, 25 June 2014 (UTC)
+ 300 − 40 + 2 = 262. This begs the question. Using this method, how is one supposed to know that 300-40=260? It seems at least one step is missing. Kdammers ( talk) 06:29, 27 November 2014 (UTC)
"Subtraction is anti-commutative, meaning that one can reverse the terms in a difference left-to-right, and the result is the negative of the original result. Symbolically, if a and b are any two numbers, then a - b = b - a. " Have I forgotten all my math or is old age dementia clouding my understanding? Or maybe it's my vision. This looks patently wrong to me. The text says the value of the two differences is opposite in sign (i.e., |a-b| = |b-a|. Right, that's clear. But then it continues with an example that shows to my eyes some-thing quite different, .i.e., that the differences not only have the same absolute value but the same value, which is only true for a few special cases, i.e., where a=b. Since this part of the article seems to have been around for some time, I am loathe to change it even though I just cannot at all see how it can be correct. E.g., let a=5 and b=2. Then a-b=5-2=3 and b-a=2-5=-3, 3NOT=-3. Hence a-bNOT [necessarily]=b-a. Or am I blind or crazy????? Kdammers ( talk) 07:49, 27 November 2014 (UTC)
Try subtracting this:
1005
-928
Notice that you are left with only 7. You cannot barrow after you turn the 5 into a 15, as the "1" in 1005 is consumed. On a calculator, it would be 77. Is there a way around this stuck? Joeleoj123 ( talk) 23:16, 26 February 2016 (UTC)
continuing the borrow leftwards until there is a non-zero digit from which to borrowshould mean that you take from the tens, making -1, then from the hundreds, making the tens column 9, but the hundreds now -1, which is immediately made up by taking the 1 from the thousands. For the subtraction above, you should have something like this, based on the article explanation, if it isn't too confusing:
9 9
1 0 0 15
- 9 2 8
________
7 7
Wcherowi has reverted the {{cn}} that I associated with the claim that "In advanced algebra ... an expression involving subtraction like A − B is generally treated as a shorthand notation for the addition A + (−B)." Minimally, a claim that a usage is "general" implies that it is used more than half the time. This is an empirical claim; why should it not need a citation? The edit summary says this usage is "standard", but this term is open to the same problem as "generally". Subtraction can be taken as primitive and −x defined as the result of subtracting x from the additive identity. What is the source for the implication that this is nonstandard? If there is one, it should be included in a citation. Peter Brown ( talk) 19:33, 21 June 2019 (UTC)
A century ago, it was common to teach compound subtraction as an explicit method during arithmetic. Examples of this include taking measurements in cups, tablespoons, and teaspoons and subtract, or to take an age at death and the date of death and work out the age it birth. Efficient methods for hand calculation were taught, and there are also some subtleties: for instance, the inferred age at birth from compound subtraction depends on the order in which the subtract is done, i.e., whether the days, months, and years are subtracted first, second, or third. There are numerous (old) books and articles on the subject, plenty enough that it should be covered somewhere on Wikipedia. My question: should it be a subtopic of this page, or should it have its own page? Barryriedsmith ( talk) 20:57, 13 September 2021 (UTC)
Subtrahend derived from 'subtrahendus' means 'to be taken away. Minuend derived from 'minuendus' means 'to be lessed/reduced'. Minus means 'less' These are given in wikipedia and other websites. For example 10 - 3 = 7, here - 3 in words minus 3 which means less 3. It means 3 is 'to be lessed'. It means 3 is the minuend by the meaning. Considering another example a boy is expected to be taken 10 marks. But he takes 7 marks, in other words the boy took '3 marks less'. This means '3 less' to 10. It means 3 is the number 'to be lessed'. So 3 is the 'minuend' by the meaning. Here expected 10 'to be taken'. So by the meaning 10 is the 'subtrahend'. Inkartumac ( talk) 09:16, 13 February 2022 (UTC)
An editor has identified a potential problem with the redirect
Restar and has thus listed it
for discussion. This discussion will occur at
Wikipedia:Redirects for discussion/Log/2022 February 15#Restar until a consensus is reached, and readers of this page are welcome to contribute to the discussion. ~~~~
User:1234qwer1234qwer4 (
talk) 20:19, 15 February 2022 (UTC)
Are there any specific claims that need citations? At least give me 3. - S L A Y T H E - ( talk) 05:52, 27 December 2022 (UTC)
{{
no footnotes|section}}
at the beginning ot sections
§ Of integers and real numbers,
§ Properties and
§ In computing. For the other sections, there are enough citations, even if many of them are not
WP:reliable sources and could be tagged with {{
better source needed}}.
D.Lazard (
talk) 10:48, 27 December 2022 (UTC)