0 If x 0, then
q 
such that x = 0 q,
for 0 q = 0 
q .Since there is no q, the definition does not apply.
0, where x is any
real number. To be sure x 0 is undefined, we
need only check the two equivalent definitions of division. Definition
[46] states that if there is a unique q such that x = yq, then x
y = q. Let y = 0 in this definition. If there
exists a unique q such that x = 0 q, then x 0
= q.
Case I: x 0 If x 0, then
q such that x = 0 q,
for 0 q = 0 q .
Since there is no q, the definition does not apply.
Case II: x = 0 If x = 0, then every q satisfies
the equation x = y q, for 0 = 0 q
q .
Since there is no unique
q, the definition does not apply.
Definition [47] states that if y 0, then
x y = xy*. Since y = 0,
this definition does not apply either.