Thread: identity proof

I was confused on how to prove/disprove that double addition operator has an identity element? #:double addition +: normal addition

a # b = 2a + 2b

I was confused on how to go about it... Should i assume that there is an identity element E

and say that

a # E = 2a + 2E = 2a?

What is the identity element for addition?

Ya it was so simple, the element is 0 for scalar addition
After a while of going in circles over, i should have just kept it simple:

a # E = 2a + 2E = 2a which is not equal to a in general: disproved

example:
a = 1 ; e = 0

1 # 0 = 2(1) + 2(0) = 2 not 1