Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

About the definition of binary operation on a set, in my notes it says a binary operation on S is a map $*:S\times S\to S$, it does not have to be a function, it is a mapping. But in the textbook, it says while defining a binary operation on a set $S$, we must be sure that exactly one element is assigned to each possible ordered pair of elements. Doesn't that mean it is a function? I am confused here, does a binary operation have to be a function? Thanks

share|improve this question
    
Usually, map (mapping) and function mean exactly the same. How do they differ in your notes? –  Tobias Kildetoft Mar 11 '13 at 17:32
    
in my notes, it explicitly says that it is just a map, not a function. What i understand from this sentence is, more than one element can be assigned to a pair –  bigO Mar 11 '13 at 17:33
2  
We can’t answer the question until we know exactly how the terms mapping and function have been defined for you. In most contexts either they mean exactly the same thing, or mappings are functions with some additional property; in neither case is it possible to have a mapping that is not a function. –  Brian M. Scott Mar 11 '13 at 17:35
    
You still haven't told us why you think a mapping and a function are different things. –  Thomas Andrews Mar 11 '13 at 17:36
1  
That’s wrong by any definition of mapping that I’ve ever encountered. –  Brian M. Scott Mar 11 '13 at 17:39
show 6 more comments

1 Answer 1

up vote 3 down vote accepted

A binary operation on $S$ is a function $S\times S\to S$. You are correct.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.