Condition in Arden's rule According to Arden's rule, the language equation $X= AX\cup B$, with unknown $X$, has the solution $X=A^*B$, provided $A$ does not contain the empty string.

My question: what is the problem with the empty string here? Can you illustrate this with a concrete example (which lacks in Wikipedia on this topic).
Consider, for instance, $A = \{ \varepsilon \}$. Then $X = AX$, so $X = AX \cup B$ holds for any $X$ with $B \subseteq X$.