- #1
Salamon
- 36
- 0
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.
"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.