At first glance it seems possible to define a/0 by considering the limit of a/b as b approaches 0.
For any positive a, the limit from the right is
however, the limit from the left is
and so the is undefined (the limit is also undefined for negative a).
Furthermore, there is no obvious definition of 0/0 that can be derived from considering the limit of a ratio. The limit
does not exist. Limits of the form
in which both ƒ(x) and g(x) approach 0 as x approaches 0, may equal any real or infinite value, or may not exist at all, depending on the particular functions ƒ and g (see l'Hôpital's rule for discussion and examples of limits of ratios). These and other similar facts show that the expression 0/0 cannot be well-defined as a limit.