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.

Need quick help with a homework question:

Determine whether the description of # is a valid definition of a binary operation on a set:

a) On $\Bbb R$ where $a\#b$ is $a*b$ (ordinary multiplication)

b) On $\Bbb Z$, where $a\#b$ is $ab^2$

Can anybody help me solve this and possibly make me understand?

share|improve this question
1  
Are you saying that you can't square an integer? –  Federica Maggioni Apr 22 '13 at 10:53
    
I don't know how to format it here where the b appears as a superscript –  Jurgen Malinao Apr 22 '13 at 10:57
1  
so did you mean $a#b=a^b$? If so, # is not a binary operation, as an example $2#-1$ is not an integer –  Federica Maggioni Apr 22 '13 at 11:01

2 Answers 2

A binary operation on a set $X$ is a map from $X\times X$ to $X$. Therefore to assure that a description yields a binary operation you should check that it is correct for each $(a,b)\in X\times X$ and for every such pair $(a,b)$ it describes an element from $X$ (all these conditions are satisfied for both your cases a) and b), so you have descriptions of binary operations).

share|improve this answer

A binary operator is a type of function. So, the question becomes, are $ab$ and $ab^2$ defined on all of $\Bbb R^2$ and $\Bbb Z^2$ respectively, and do they produce unique values in $\Bbb R$ and $\Bbb Z$ respectively?

See: http://en.wikipedia.org/wiki/Binary_operation

share|improve this answer

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.