It is kind of tricky to define this situation formally. Much like if a statement says "Given a list of numbers" than does empty list denotes a list of numbers?

It is kind of tricky to define this situation formally. Much like if a statement says "Given a list of numbers" than does empty list denotes a list of numbers? There are arguments for both - yes it does and no it doesn't - but the only way to select any one argument over other without conflict depends on additional constraints in the definition like saying "Given a list of numbers where the minimum length of list is 1".