What does it mean to add a number to a set?

Question

I have the following problem:

Show that the interval $[0,1]$ cannot be partitioned into two disjoint sets $A$ and $B$ such that $B=A+a$ for some real number $a$.

My question is what does $B=A+a$ mean in this context? Does it mean $B=A\cup\{a\}$? Or something else?

Answer 1

$A+a=\{x+a: x \in A\}$. Not a union but an algebraic sum.