There's also
binary function. Merge them? --
JanHidders
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
binary operation article from scratch I would have only allowed it to cover functions of the form f : S x S -> S, rather than the general f : S x T -> 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
binary function and
binary operation.
Zundark, 2001-08-08
I agree, binary operations are S x S -> 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
Oh, you guys don't consider the vector scalar product (V * V -> R) or scaling of vectors (R * V -> V) or matrices ( R * M -> M ), etc to be binary operations? --
Buz Cory
Perhaps we should ask "what would Eric Weisstein" have done?" :-) But he doesn't seem to be sure either. There is
http://www.google.com/search?q=cache:LSEQ3bRAKkI:br.crashed.net/~akrowne/crc/math/b/b211.htm+binary+operator+eric+weisstein&hl=en
and there is
http://www.google.com/search?q=cache:FjdWL0BZpB4:www.math.pku.edu.cn/library/encyclopedia/contents/BinaryOperator.html+binary+operator+eric+weisstein&hl=en
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:
- begin with S x S -> S definition
- something about the notation
- a remark that sometimes also S x T -> U is possible, with Buz' examples and ref. to binary function
--
JanHidders
Maybe we should distinguish between a binary operation
on a set (S x S->S) and a binary operation as such (S x T->U)?
I don't know. --
AxelBoldt
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 ->S) makes more sense.
WMORRIS
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