There exists a unique integer a such that a + b = b for all integers b.

Question

I am doing this for a proofs class and I keep getting confused about how to prove it

Answer 1

The unique number a is the number 0, since for all integers b we have 0+b=b. To see the uniqueness assume that there are two of them, say x and y. Then, you have that x+y=y which implies x=y.