Sum of an empty set and a finite set. Can we define the sum of an empty set and a finite set$?$
For example -
If $A= \{1,2\} , B= \emptyset$
Then what is $A+B$.
My intuition says it should be $A$.
But I couldn't find any proper reason behind it.

If by $A+B$ you mean $\{\,a+b\mid a\in A,b\in B\,\}$, then if $B$ is empty there is no $b\in B$ so there are no elements in $A+B$. "$B$ is empty" is very different from "zero is in $B$".
