938:. Also, the most elementary relations (equality and inequalities) are presented after the divisibility relation (much more technical), and the example of inequalities between numbers are not clearly presented (only their generalizations to various areas are explicitly mentioned). In the body, the properties that are used in all mathematics (for example reflexivity, transitivity, symmetry and anti-symmetry) are defined after or between much more technical properties that are known and used only by specialists of relations and graphs.
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identity can be extended to an operation on finite sequences whose value on the empty sequence is the left identity and whose value on a sequence {a:0 <= i < k+1} of length k + 1 is Sk (+) a, where Sk is the value of the operation on the leading subsequence (prefix) {a:0 <= i < k} of length k.
530:
Is the line: "If the operation is commutative, ab = ba, then the value depends only on the multiset a,b,c." Meant to have (a,b),c, where a and b must be together. For it to not matter where c comes in terms of a and b, i.e between a and b, then wouldn't it also require associativity, where it doesn't
394:
Moreover, what I would really like to see is the generic name for this new operation, which is what I was looking for when I came to this page. I've found the terms "bulk action", "iterated binary operation", and "prefix operation" through google, but haven't seen any clear evidence that any of these
967:
I feel are inapplicable as those terms are linked to articles which define them. I think a short listing of commonly-named symmetry properties would be a useful addition to this article, as they help connect to a variety of algebraic structures, and I cannot find any such listing on
Knowledge either
390:
I would like to see a discussion of the extension of a binary operator to finite sequences through repeated application. For example, the addition operator can be extended to the sum operation, the multiplication operator to the product operation, etc. In general, any binary operator (+) with a left
1024:
This is not a WP inconsistency. This an inconsistency of the common mathematics terminology. This is rather common for mathematical concepts that need not to be formally defined, because one considers only specific example, without considering the whole class of objects. Nevertheless, I have edited
404:
I don't think "iterated binary operation" would belong in a page about binary operations since it requires a unique left identitity and in the prototypical cases of sum and product notation requires associativity. However a link to such a page would be appropriate if someone who knows enough about
998:
The article is rather vague about it. Could one explain it somehow better, like "usually binary operation means f: A × A → A, while f: A × B → C is called binary function, but sometimes binary operation means f: A × B → C, while f: A × A → A is called internal binary operation" (I am not sure that
488:
is necessary in a binary operation from this article. The first paragraph leads one to believe that closure is not required, but then the more precise definition that follows leads one to believe closure is required. Then the article flips back and describes situations where closure is not
284:
a set' and 'General binary functions' alternatives; there is an added section covering some of the 'other' binary operations. However, it does not solve the issue. First of all, I wonder if there hasn't been a confusion between 'scalar product', mentioned as an example supra, and 'scalar
504:
The subject of closure is discussed in the above section of this Talk page. The current article defines "binary operation on a set" rather than "binary operation". It would be best to point out in the article that the phrase "on a set" is an important
424:
I think you're describing "folding". This is a common notion in functional programming languages, used for recursing (iterating) over data types such as sequences and trees. The only description I can find in
Knowledge is the article
170:
I'm not sure they really mean the same thing. A binary operation is usually an algebraic operation, and is often denoted more like a*b than f(a,b). Probably the article ought to explain this. Also, if I had written the
222:
which doesn't explicitly require the input domains to be the same. I know that in my own field (computer science) the term is used for any operator that needs two arguments. Perhaps it should be someting like this:
360:
Actually, the restriction to the two singly enumerated instances in the present article are not only in conflict with some literature, but with a number of
Knowledge items in the category 'Binary operation'; e.g.,
357:. Some (but far from all) modern textbooks instead use the terms 'dot product' and 'scalar multiplication', respectively. In my opinion, both functions are legitimate candidates for the term 'binary operation'.
914:(relation between their two arguments and their result). However WP articles should be written to be accessible to the largest possible audience, and must proceed by increasing degree of technicality (see
258:
My textbook doesn't agree with the definition used on this article. I guess it is rather a convention or terminology problem than a real issue. It defines a binary operation as "f:AxA -: -->
217:
695:
These two articles appear to cover the same subject, but neither so much as reference or link to the other. I'm inclined to suggest that they be merged together. Thoughts/questions/concerns? --
510:
The article defines "external binary operation" and this may give readers the impression that an "external binary operation" is a more general mathematical object that a "binary operation".
140:
380:
protest, I suggest that he or she briefs through all the items in the category, and lists those that should be omitted or rewritten, if we are to retain the present restricted definition.
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required. I think the real issue is that the term has been overloaded such that it means slightly different things in different contexts, but this should somehow be made more clear.
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I agree with D.Lazard, the only thing in common with these articles is the word "binary". The reason there are no links between these articles is that there are no connections. --
762:
I agree with D.Lazard and Bill
Cherowitzo. From a computer-science point of view, a binary relation could be considered as a special case of a binary operation, with result type
192:
S. This article simply describes functions with two arguments. I think it should be changed, and the popular infix notation a*b for *(a,b) should be mentioned. --AxelBoldt
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I think you are onto something, Axel. Binary operation on a set requires closure for the result, and the elements chosen must also be from the set, so (S x S -: -->
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Therefore, if no one protests, I think we should change the item, noting that the term is used in different senses in different contexts, sometimes very broadly,
218:
http://www.google.com/search?q=cache:FjdWL0BZpB4:www.math.pku.edu.cn/library/encyclopedia/contents/BinaryOperator.html+binary+operator+eric+weisstein&hl=en
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130:
766:. However, in mathematics (in particular in 1st-order predicate logic), operations and relations are usually considered completely different things. -
429:, which is the same concept disguised by category theory. However, there should be plenty of stuff on the web if you search for "fold" and "unfold". --
1051:
734:. Basic examples are =, ≠, <, ≤, ... There are absolutely no reason for a merge. On the contrary, a merge would be confusing for most readers.
531:
matter if you do a and b first, or b and c? The next line states it depends only on the multiset a,b,c if it is both associative and commutative.
106:
576:
The article says "More precisely, a binary operation on a set S is a binary relation that maps elements of the
Cartesian product S × S to S"
271:
Well, from further research, it is actually quite unique to my university. Popular definition in most universities in Israel is f:AxA -: -->
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a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.
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includes the requirement for closure of course, again, conflicting with the Group article. This is the convention in Israel, I guess.. --
876:. However, I understand your point that they describe different things. I would then propose the article be extended or rewritten to be
594:
177:
U. I didn't like to change the original too much, but perhaps it should be changed. In any case it would be a good idea to cross-link
714:
takes two elements and returns a third one, generally in the same set. The basic examples are addition (+) and multiplication (×). A
210:
http://www.google.com/search?q=cache:LSEQ3bRAKkI:br.crashed.net/~akrowne/crc/math/b/b211.htm+binary+operator+eric+weisstein&hl=en
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multiplication', which now is given as an example in the article. In classical terminology, 'scalar product' is a function
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Perhaps we should ask "what would Eric
Weisstein" have done?" :-) But he doesn't seem to be sure either. There is
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Well binary operations could be considered a kind of binary relation. Specifically, they are subsets of
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884:, containing a short listing of all the symmetry properties that a binary operation can have, like the
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contains many terms that are known only by people having a very good mathematical knowledge, such as
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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article from scratch I would have only allowed it to cover functions of the form f : S x S -: -->
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an operation is an action or procedure which produces a new value from zero or more input values
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325:, in this context mostly the real numbers); while 'multiplication with scalars' is a function
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a binary operation is an action or procedure which produces a new value from two input values
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I think both articles could stand to be rewritten, although some of your critiques of
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an operation is a calculation from zero or more input values to an output value
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No, binary operations cannot be considered as binary relations, as they are
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a binary operation is calculation from two input values to an output value
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OK, I bit the bullet and added a new page myself. It probably needs help.
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At present, there seems to be a compromise between the 'Only operations
583:? This isn't even mentioned in the article. Instead it says it is a
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Oh, you guys don't consider the vector scalar product (V * V -: -->
926:, although the former may be improved. For example, the lead of
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the article for making clear that both terminologies are used.
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U is possible, with Buz' examples and ref. to binary function
850:, and for "external binary operations" relaxes that to just
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this is true)? There is certainly an inconsistency between
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Isn't this a special case of a binary operation? Surely a
647:. Thus a binary operation is surely defined as follows:
1003:, where f: A × A → B is called a binary operation, and
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Maybe we should distinguish between a binary operation
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I fixed it, intended formatting changed the meaning.--
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B". Where closure isn't required. The definition of a
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So, if an article deserves to be rewritten, this is
661:. This enables a binary operation to be defined as:
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994:Is it f: A × A → A, f: A × A → B or f: A × B → C?
657:I actually favour a revision to operation too:
587:, wich is not a function so should be wrong.
248:S) and a binary operation as such (S x T-: -->
484:It is very tough to determine whether or not
8:
643:? Recalling the definition of an operation:
191:I agree, binary operations are S x S -: -->
176:S, rather than the general f : S x T -: -->
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579:Isn't a binary operation supposed to be a
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710:These are completely different things: a
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234:a remark that sometimes also S x T -: -->
968:as an article, category, or infobox. --
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350:{\displaystyle R\times V\rightarrow V}
310:{\displaystyle V\times V\rightarrow R}
197:R) or scaling of vectors (R * V -: -->
718:takes also two elements, but returns
7:
458:--No mention of blob-- The symbol?
376:in the Knowledge notes. If any one
199:M ), etc to be binary operations? --
95:This article is within the scope of
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321:is a vector space over the scalars
38:It is of interest to the following
609:You are right. This is now fixed.
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115:Knowledge:WikiProject Mathematics
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118:Template:WikiProject Mathematics
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254:S) makes more sense. WMORRIS
135:This article has been rated as
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619:04:47, 30 September 2012 (UTC)
438:Oh! I just found your article
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249:U)? I don't know. --AxelBoldt
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959:19:13, 28 November 2018 (UTC)
906:18:17, 28 November 2018 (UTC)
776:21:01, 26 November 2018 (UTC)
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705:17:46, 26 November 2018 (UTC)
681:12:08, 2 September 2015 (UTC)
474:21:35, 26 February 2008 (UTC)
410:01:50, 13 February 2006 (UTC)
198:V) or matrices ( R * M -: -->
109:and see a list of open tasks.
978:20:54, 3 December 2018 (UTC)
934:(in the first sentence), or
896:, and so forth. Thoughts? --
520:17:55, 22 January 2015 (UTC)
444:Fold (higher-order function)
400:18:36, 28 October 2005 (UTC)
231:something about the notation
166:. Merge them? -- JanHidders
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818:. The introduction assumes
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405:it is willing to write it.
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