# Thread: What definition do them mean?(Binary Operation)

1. ## What definition do them mean?(Binary Operation)

I am talking about the (a) part. It says by the definition... What definition? How am I supposed to prove that it is commutative when no variable is given or function is defined?

2. ## Re: What definition do them mean?(Binary Operation)

Originally Posted by abhistud

I am talking about the (a) part. It says by the definition... What definition? How am I supposed to prove that it is commutative when no variable is given or function is defined?
the definition that

$a * b = 1, ~\forall a,b \in \mathbb{R}$

if $a * b = 1~\forall a,b \in \mathbb{R}$

then I can swap $a$ and $b$ and get

$b * a = 1$

$a * b = 1 = b*a$

$a*b = b*a$

3. ## Re: What definition do them mean?(Binary Operation)

Hey abhistud.

Following on from what romsek said - you have to show that swapping and a and b doesn't change the result when you apply the operation.

4. ## Re: What definition do them mean?(Binary Operation)

I see. Thanks for the help.