Quick question about identity elements

[Salamon]

I saw this question in an abstract algebra text that I was reading.

"Is it true that (w − x) − (y − z) = (w − y) − (x − z) is an identity for real numbers?
Can you say why or why not?"

I know that an identity element does not change the value of a real number. So 0 is the identity element for addition and 1 is the identity element for multiplication.

But how can an equation be an identity element?

I mean I see that (w-x)-(y-z) = (w-y)-(x-z) is a true statement. But unless you know the values of w,x,y,and z, how can you see whether it will be an identity element for real numbers.

 

[mathman]

You misunderstand the statement. It calls the equation an identity, meaning that it holds for all real values of x, y, z, and w. It has nothing to do with the identity element (0) as such.

 

[Salamon]

thanks